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The crystal structure of the synthetic double carbonate norsethite [BaMg(CO3)2] has been reinvestigated using X-ray diffraction data within the temperature range 100–500 K using a high-sensitivity PILATUS pixel detector. The previously assumed positional shift of the crystallographically unique oxygen atom is confirmed. The shift is associated with a coupled rotation of symmetry-equivalent carbonate groups. It was possible to follow the shift using high-accuracy experiments under varying temperature conditions between 100 K and the critical transition temperature occurring at Tc = 363 ± 3 K. The transition of the α-form (space group R{\bar 3}c; below Tc), which represents a superstructure of the β-form (space group R{\bar 3}m, with c′ = c/2; above Tc) was studied in detail. The tricritical order character of this displacive phase transition was verified by tracking the intensities of the recorded superstructure reflections (l = 2n + 1) from single-crystal diffraction and using high-precision lattice parameters obtained from powder diffraction in transmission geometry. Thermodynamic properties suggest both rotation of the CO3 group and a coordination change of the BaO12 coordination polyhedra as the order parameters driving the temperature-dependent α–β phase transition. Nevertheless, a detailed structural analysis reveals the coordination change of the barium atoms to be the main driving force for the observed transformation.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S2052520617009295/xk5041sup1.cif
Contains datablocks norse_100, norse_150, norse_200, norse_250, norse_280, norse_299, norse_320, norse_330, norse_340, norse_350, norse_360, norse_370, norse_380, norse_390, norse_400, norse_420, norse_440, norse_460, norse_480, norse_500

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Portable Document Format (PDF) file https://doi.org/10.1107/S2052520617009295/xk5041sup22.pdf
Supplementary material

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_100sup2.hkl
Contains datablock norse_100

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_150sup3.hkl
Contains datablock norse_150

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_200sup4.hkl
Contains datablock norse_200

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_250sup5.hkl
Contains datablock norse_250

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_280sup6.hkl
Contains datablock norse_280

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_299sup7.hkl
Contains datablock norse_299

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_320sup8.hkl
Contains datablock norse_320

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_330sup9.hkl
Contains datablock norse_330

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_340sup10.hkl
Contains datablock norse_340

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_350sup11.hkl
Contains datablock norse_350

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_360sup12.hkl
Contains datablock norse_360

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_370sup13.hkl
Contains datablock norse_370

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_380sup14.hkl
Contains datablock norse_380

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_390sup15.hkl
Contains datablock norse_390

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_400sup16.hkl
Contains datablock norse_400

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_420sup17.hkl
Contains datablock norse_420

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_440sup18.hkl
Contains datablock norse_440

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Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_460sup19.hkl
Contains datablock norse_460

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_480sup20.hkl
Contains datablock norse_480

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_500sup21.hkl
Contains datablock norse_500

CCDC references: 1557350; 1557351; 1557352; 1557353; 1557354; 1557355; 1557356; 1557357; 1557358; 1557359; 1557360; 1557361; 1557362; 1557363; 1557364; 1557365; 1557366; 1557367; 1557368; 1567750

Computing details top

For all structures, program(s) used to refine structure: SHELXL2014/7 (Sheldrick, 2014).

(norse_100) top
Crystal data top
C6Ba3Mg3O18Dx = 3.868 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 9285 reflections
a = 5.0083 (1) Åθ = 1.5–45°
c = 33.3987 (8) ŵ = 8.30 mm1
V = 725.51 (3) Å3T = 100 K
Z = 2Prismatic
F(000) = 7680.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.030
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.6°, θmin = 3.7°
Tmin = 0.7, Tmax = 0.8h = 109
9285 measured reflectionsk = 109
692 independent reflectionsl = 6534
535 reflections with I > 2σ(I)
Refinement top
Refinement on F217 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.010 w = 1/[σ2(Fo2) + (0.012P)2]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.021(Δ/σ)max < 0.001
S = 1.01Δρmax = 0.54 e Å3
692 reflectionsΔρmin = 0.58 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.25000.00471 (2)
Mg20.00000.00000.00000.00457 (7)
O30.11020 (13)0.81779 (13)0.12928 (2)0.00912 (9)
C40.00000.00000.13043 (3)0.00515 (11)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.00405 (2)0.00405 (2)0.00603 (3)0.00203 (1)0.0000.000
Mg20.00406 (11)0.00406 (11)0.00558 (16)0.00203 (5)0.0000.000
O30.0118 (2)0.0095 (2)0.01034 (17)0.0085 (2)0.00348 (15)0.00195 (14)
C40.00497 (17)0.00497 (17)0.0055 (2)0.00248 (8)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.7904 (5)Mg2—O3xviii2.0558 (6)
Ba1—O3ii2.7904 (5)Mg2—Ba1xix4.0135 (1)
Ba1—O3iii2.7904 (6)Mg2—Ba1xx4.0135 (1)
Ba1—O3iv2.7904 (6)Mg2—Ba1xxi4.0135 (1)
Ba1—O3v2.7904 (5)Mg2—Ba1xxii4.0135 (1)
Ba1—O3vi2.7904 (5)Mg2—Ba1iii4.0135 (1)
Ba1—O3vii3.0971 (6)Mg2—Ba1xxiii4.0135 (1)
Ba1—O3viii3.0971 (6)O3—C4xxiv1.2816 (6)
Ba1—O3ix3.0972 (6)O3—Mg2xxv2.0559 (6)
Ba1—O3x3.0972 (6)O3—Ba1iii2.7904 (5)
Ba1—O3xi3.0972 (6)O3—Ba1x3.0972 (6)
Ba1—O3xii3.0972 (6)C4—O3xxvi1.2816 (6)
Mg2—O3xiii2.0558 (6)C4—O3xxvii1.2816 (6)
Mg2—O3xiv2.0558 (6)C4—O3xxviii1.2816 (6)
Mg2—O3xv2.0558 (6)C4—Ba1xxi3.2916 (4)
Mg2—O3xvi2.0558 (6)C4—Ba1xx3.2916 (4)
Mg2—O3xvii2.0558 (6)C4—Ba1iii3.2916 (4)
O3i—Ba1—O3ii123.74 (2)O3xiv—Mg2—O3xviii86.95 (2)
O3i—Ba1—O3iii137.64 (2)O3xv—Mg2—O3xviii93.05 (2)
O3ii—Ba1—O3iii92.660 (17)O3xvi—Mg2—O3xviii86.95 (2)
O3i—Ba1—O3iv92.660 (17)O3xvii—Mg2—O3xviii180.00 (4)
O3ii—Ba1—O3iv137.64 (2)O3xiii—Mg2—Ba1xix40.505 (15)
O3iii—Ba1—O3iv67.23 (2)O3xiv—Mg2—Ba1xix139.495 (15)
O3i—Ba1—O3v92.659 (17)O3xv—Mg2—Ba1xix49.391 (16)
O3ii—Ba1—O3v67.23 (2)O3xvi—Mg2—Ba1xix130.609 (16)
O3iii—Ba1—O3v123.74 (2)O3xvii—Mg2—Ba1xix98.493 (17)
O3iv—Ba1—O3v92.658 (17)O3xviii—Mg2—Ba1xix81.507 (17)
O3i—Ba1—O3vi67.23 (2)O3xiii—Mg2—Ba1xx139.495 (15)
O3ii—Ba1—O3vi92.659 (17)O3xiv—Mg2—Ba1xx40.505 (15)
O3iii—Ba1—O3vi92.658 (17)O3xv—Mg2—Ba1xx130.609 (16)
O3iv—Ba1—O3vi123.74 (2)O3xvi—Mg2—Ba1xx49.391 (16)
O3v—Ba1—O3vi137.64 (2)O3xvii—Mg2—Ba1xx81.507 (17)
O3i—Ba1—O3vii176.304 (11)O3xviii—Mg2—Ba1xx98.493 (17)
O3ii—Ba1—O3vii57.15 (2)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii43.90 (2)O3xiii—Mg2—Ba1xxi81.507 (17)
O3iv—Ba1—O3vii85.188 (13)O3xiv—Mg2—Ba1xxi98.493 (17)
O3v—Ba1—O3vii84.451 (13)O3xv—Mg2—Ba1xxi139.494 (15)
O3vi—Ba1—O3vii116.470 (19)O3xvi—Mg2—Ba1xxi40.506 (15)
O3i—Ba1—O3viii57.15 (2)O3xvii—Mg2—Ba1xxi130.609 (16)
O3ii—Ba1—O3viii176.304 (11)O3xviii—Mg2—Ba1xxi49.391 (16)
O3iii—Ba1—O3viii85.188 (13)Ba1xix—Mg2—Ba1xxi102.791 (1)
O3iv—Ba1—O3viii43.90 (2)Ba1xx—Mg2—Ba1xxi77.209 (1)
O3v—Ba1—O3viii116.470 (19)O3xiii—Mg2—Ba1xxii98.493 (17)
O3vi—Ba1—O3viii84.451 (13)O3xiv—Mg2—Ba1xxii81.507 (17)
O3vii—Ba1—O3viii122.24 (2)O3xv—Mg2—Ba1xxii40.506 (15)
O3i—Ba1—O3ix43.90 (2)O3xvi—Mg2—Ba1xxii139.494 (15)
O3ii—Ba1—O3ix84.450 (13)O3xvii—Mg2—Ba1xxii49.391 (16)
O3iii—Ba1—O3ix176.304 (12)O3xviii—Mg2—Ba1xxii130.609 (16)
O3iv—Ba1—O3ix116.470 (19)Ba1xix—Mg2—Ba1xxii77.209 (1)
O3v—Ba1—O3ix57.15 (2)Ba1xx—Mg2—Ba1xxii102.791 (1)
O3vi—Ba1—O3ix85.190 (13)Ba1xxi—Mg2—Ba1xxii180.0
O3vii—Ba1—O3ix134.87 (2)O3xiii—Mg2—Ba1iii130.609 (16)
O3viii—Ba1—O3ix97.574 (13)O3xiv—Mg2—Ba1iii49.391 (16)
O3i—Ba1—O3x84.450 (13)O3xv—Mg2—Ba1iii81.507 (16)
O3ii—Ba1—O3x43.90 (2)O3xvi—Mg2—Ba1iii98.493 (16)
O3iii—Ba1—O3x116.470 (19)O3xvii—Mg2—Ba1iii139.495 (15)
O3iv—Ba1—O3x176.304 (12)O3xviii—Mg2—Ba1iii40.506 (15)
O3v—Ba1—O3x85.190 (13)Ba1xix—Mg2—Ba1iii102.791 (1)
O3vi—Ba1—O3x57.15 (2)Ba1xx—Mg2—Ba1iii77.209 (1)
O3vii—Ba1—O3x97.574 (13)Ba1xxi—Mg2—Ba1iii77.209 (1)
O3viii—Ba1—O3x134.87 (2)Ba1xxii—Mg2—Ba1iii102.791 (1)
O3ix—Ba1—O3x59.83 (2)O3xiii—Mg2—Ba1xxiii49.391 (16)
O3i—Ba1—O3xi85.189 (13)O3xiv—Mg2—Ba1xxiii130.609 (16)
O3ii—Ba1—O3xi116.470 (19)O3xv—Mg2—Ba1xxiii98.493 (16)
O3iii—Ba1—O3xi57.15 (2)O3xvi—Mg2—Ba1xxiii81.507 (16)
O3iv—Ba1—O3xi84.452 (13)O3xvii—Mg2—Ba1xxiii40.506 (15)
O3v—Ba1—O3xi176.304 (12)O3xviii—Mg2—Ba1xxiii139.495 (15)
O3vi—Ba1—O3xi43.89 (2)Ba1xix—Mg2—Ba1xxiii77.209 (1)
O3vii—Ba1—O3xi97.574 (13)Ba1xx—Mg2—Ba1xxiii102.791 (1)
O3viii—Ba1—O3xi59.83 (2)Ba1xxi—Mg2—Ba1xxiii102.791 (1)
O3ix—Ba1—O3xi122.24 (2)Ba1xxii—Mg2—Ba1xxiii77.209 (1)
O3x—Ba1—O3xi97.573 (13)Ba1iii—Mg2—Ba1xxiii180.0
O3i—Ba1—O3xii116.470 (19)C4xxiv—O3—Mg2xxv138.67 (5)
O3ii—Ba1—O3xii85.189 (13)C4xxiv—O3—Ba1iii101.33 (4)
O3iii—Ba1—O3xii84.452 (13)Mg2xxv—O3—Ba1iii110.90 (2)
O3iv—Ba1—O3xii57.15 (2)C4xxiv—O3—Ba1x87.11 (3)
O3v—Ba1—O3xii43.89 (2)Mg2xxv—O3—Ba1x100.35 (2)
O3vi—Ba1—O3xii176.304 (12)Ba1iii—O3—Ba1x116.471 (19)
O3vii—Ba1—O3xii59.83 (2)O3xxvi—C4—O3xxvii119.913 (5)
O3viii—Ba1—O3xii97.574 (13)O3xxvi—C4—O3xxviii119.911 (5)
O3ix—Ba1—O3xii97.573 (13)O3xxvii—C4—O3xxviii119.911 (5)
O3x—Ba1—O3xii122.24 (2)O3xxvi—C4—Ba1xxi70.01 (3)
O3xi—Ba1—O3xii134.87 (2)O3xxvii—C4—Ba1xxi148.77 (6)
O3xiii—Mg2—O3xiv180.00 (4)O3xxviii—C4—Ba1xxi56.22 (3)
O3xiii—Mg2—O3xv86.95 (2)O3xxvi—C4—Ba1xx148.77 (6)
O3xiv—Mg2—O3xv93.05 (2)O3xxvii—C4—Ba1xx56.22 (3)
O3xiii—Mg2—O3xvi93.05 (2)O3xxviii—C4—Ba1xx70.01 (3)
O3xiv—Mg2—O3xvi86.95 (2)Ba1xxi—C4—Ba1xx99.066 (18)
O3xv—Mg2—O3xvi180.00 (4)O3xxvi—C4—Ba1iii56.22 (3)
O3xiii—Mg2—O3xvii86.95 (2)O3xxvii—C4—Ba1iii70.01 (3)
O3xiv—Mg2—O3xvii93.05 (2)O3xxviii—C4—Ba1iii148.77 (6)
O3xv—Mg2—O3xvii86.95 (2)Ba1xxi—C4—Ba1iii99.065 (18)
O3xvi—Mg2—O3xvii93.05 (2)Ba1xx—C4—Ba1iii99.065 (18)
O3xiii—Mg2—O3xviii93.05 (2)
Symmetry codes: (i) x+y2/3, y1/3, z+1/6; (ii) y1/3, x+y2/3, z+1/3; (iii) x1/3, y+1/3, z+1/3; (iv) y+1/3, x1/3, z+1/6; (v) x+1/3, xy+2/3, z+1/6; (vi) xy+2/3, x+1/3, z+1/3; (vii) xy+2/3, x2/3, z+1/3; (viii) x2/3, xy+2/3, z+1/6; (ix) y+4/3, x+2/3, z+1/6; (x) x+2/3, y+4/3, z+1/3; (xi) y4/3, x+y2/3, z+1/3; (xii) x+y2/3, y4/3, z+1/6; (xiii) x1/3, xy+1/3, z1/6; (xiv) x+1/3, x+y1/3, z+1/6; (xv) y+2/3, x+1/3, z1/6; (xvi) y2/3, x1/3, z+1/6; (xvii) x+y1/3, y2/3, z1/6; (xviii) xy+1/3, y+2/3, z+1/6; (xix) x2/3, y1/3, z1/3; (xx) x+2/3, y+1/3, z+1/3; (xxi) x1/3, y2/3, z+1/3; (xxii) x+1/3, y+2/3, z1/3; (xxiii) x+1/3, y1/3, z1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, z+1/6; (xxvi) x+y1, x, z; (xxvii) y+1, xy+1, z; (xxviii) x, y1, z.
(norse_150) top
Crystal data top
C6Ba3Mg3O18Dx = 3.869 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 8758 reflections
a = 5.0084 (2) Åθ = 1.5–45°
c = 33.3941 (15) ŵ = 8.30 mm1
V = 725.43 (7) Å3T = 150 K
Z = 2Prismatic
F(000) = 7680.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.030
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.6°, θmin = 3.7°
Tmin = 0.7, Tmax = 0.8h = 109
8758 measured reflectionsk = 109
692 independent reflectionsl = 6534
506 reflections with I > 2σ(I)
Refinement top
Refinement on F217 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.010 w = 1/[σ2(Fo2) + (0.0096P)2]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.020(Δ/σ)max < 0.001
S = 1.02Δρmax = 0.42 e Å3
692 reflectionsΔρmin = 0.58 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.25000.00611 (2)
Mg20.00000.00000.00000.00530 (7)
O30.11154 (14)0.81907 (14)0.12925 (2)0.01115 (11)
C40.00000.00000.13038 (3)0.00599 (11)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.00533 (2)0.00533 (2)0.00767 (3)0.00267 (1)0.0000.000
Mg20.00471 (10)0.00471 (10)0.00650 (17)0.00235 (5)0.0000.000
O30.0149 (3)0.0119 (3)0.01229 (18)0.0109 (3)0.00434 (17)0.00267 (16)
C40.00584 (17)0.00584 (17)0.0063 (3)0.00292 (8)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.7952 (6)Mg2—O3xviii2.0556 (6)
Ba1—O3ii2.7952 (6)Mg2—Ba1xix4.0132 (1)
Ba1—O3iii2.7952 (6)Mg2—Ba1xx4.0132 (1)
Ba1—O3iv2.7952 (6)Mg2—Ba1xxi4.0132 (1)
Ba1—O3v2.7952 (6)Mg2—Ba1xxii4.0132 (1)
Ba1—O3vi2.7952 (6)Mg2—Ba1xxiii4.0133 (1)
Ba1—O3vii3.0909 (6)Mg2—Ba1iii4.0133 (1)
Ba1—O3viii3.0909 (6)O3—C4xxiv1.2810 (6)
Ba1—O3ix3.0909 (6)O3—Mg2xxv2.0556 (6)
Ba1—O3x3.0909 (6)O3—Ba1iii2.7952 (6)
Ba1—O3xi3.0910 (6)O3—Ba1x3.0909 (6)
Ba1—O3xii3.0910 (6)C4—O3xxvi1.2809 (6)
Mg2—O3xiii2.0556 (6)C4—O3xxvii1.2809 (6)
Mg2—O3xiv2.0556 (6)C4—O3xxviii1.2809 (6)
Mg2—O3xv2.0556 (6)C4—Ba1xxii3.2907 (4)
Mg2—O3xvi2.0556 (6)C4—Ba1xx3.2907 (4)
Mg2—O3xvii2.0556 (6)C4—Ba1iii3.2908 (4)
O3i—Ba1—O3ii123.70 (2)O3xiv—Mg2—O3xviii86.90 (2)
O3i—Ba1—O3iii137.56 (2)O3xv—Mg2—O3xviii93.10 (2)
O3ii—Ba1—O3iii92.790 (17)O3xvi—Mg2—O3xviii86.90 (2)
O3i—Ba1—O3iv92.790 (17)O3xvii—Mg2—O3xviii180.00 (4)
O3ii—Ba1—O3iv137.56 (2)O3xiii—Mg2—Ba1xix98.477 (17)
O3iii—Ba1—O3iv67.03 (3)O3xiv—Mg2—Ba1xix81.523 (17)
O3i—Ba1—O3v92.790 (17)O3xv—Mg2—Ba1xix40.651 (16)
O3ii—Ba1—O3v67.03 (3)O3xvi—Mg2—Ba1xix139.349 (16)
O3iii—Ba1—O3v123.70 (2)O3xvii—Mg2—Ba1xix49.219 (17)
O3iv—Ba1—O3v92.789 (17)O3xviii—Mg2—Ba1xix130.781 (17)
O3i—Ba1—O3vi67.03 (3)O3xiii—Mg2—Ba1xx81.523 (17)
O3ii—Ba1—O3vi92.790 (17)O3xiv—Mg2—Ba1xx98.477 (17)
O3iii—Ba1—O3vi92.789 (17)O3xv—Mg2—Ba1xx139.349 (16)
O3iv—Ba1—O3vi123.70 (2)O3xvi—Mg2—Ba1xx40.651 (16)
O3v—Ba1—O3vi137.56 (2)O3xvii—Mg2—Ba1xx130.781 (17)
O3i—Ba1—O3vii176.440 (13)O3xviii—Mg2—Ba1xx49.219 (17)
O3ii—Ba1—O3vii57.15 (2)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii43.91 (2)O3xiii—Mg2—Ba1xxi49.218 (17)
O3iv—Ba1—O3vii85.140 (13)O3xiv—Mg2—Ba1xxi130.782 (17)
O3v—Ba1—O3vii84.430 (13)O3xv—Mg2—Ba1xxi98.477 (17)
O3vi—Ba1—O3vii116.53 (2)O3xvi—Mg2—Ba1xxi81.523 (17)
O3i—Ba1—O3viii57.15 (2)O3xvii—Mg2—Ba1xxi40.653 (16)
O3ii—Ba1—O3viii176.440 (13)O3xviii—Mg2—Ba1xxi139.347 (16)
O3iii—Ba1—O3viii85.140 (13)Ba1xix—Mg2—Ba1xxi77.216 (2)
O3iv—Ba1—O3viii43.91 (2)Ba1xx—Mg2—Ba1xxi102.784 (2)
O3v—Ba1—O3viii116.53 (2)O3xiii—Mg2—Ba1xxii130.782 (17)
O3vi—Ba1—O3viii84.430 (13)O3xiv—Mg2—Ba1xxii49.218 (17)
O3vii—Ba1—O3viii122.25 (2)O3xv—Mg2—Ba1xxii81.523 (17)
O3i—Ba1—O3ix43.91 (2)O3xvi—Mg2—Ba1xxii98.477 (17)
O3ii—Ba1—O3ix84.430 (13)O3xvii—Mg2—Ba1xxii139.347 (16)
O3iii—Ba1—O3ix176.440 (13)O3xviii—Mg2—Ba1xxii40.653 (16)
O3iv—Ba1—O3ix116.53 (2)Ba1xix—Mg2—Ba1xxii102.784 (2)
O3v—Ba1—O3ix57.15 (2)Ba1xx—Mg2—Ba1xxii77.216 (2)
O3vi—Ba1—O3ix85.141 (14)Ba1xxi—Mg2—Ba1xxii180.0
O3vii—Ba1—O3ix134.89 (2)O3xiii—Mg2—Ba1xxiii40.653 (16)
O3viii—Ba1—O3ix97.522 (14)O3xiv—Mg2—Ba1xxiii139.347 (17)
O3i—Ba1—O3x84.430 (13)O3xv—Mg2—Ba1xxiii49.219 (17)
O3ii—Ba1—O3x43.91 (2)O3xvi—Mg2—Ba1xxiii130.781 (17)
O3iii—Ba1—O3x116.53 (2)O3xvii—Mg2—Ba1xxiii98.478 (17)
O3iv—Ba1—O3x176.440 (13)O3xviii—Mg2—Ba1xxiii81.522 (17)
O3v—Ba1—O3x85.141 (14)Ba1xix—Mg2—Ba1xxiii77.215 (3)
O3vi—Ba1—O3x57.15 (2)Ba1xx—Mg2—Ba1xxiii102.785 (3)
O3vii—Ba1—O3x97.522 (14)Ba1xxi—Mg2—Ba1xxiii77.215 (2)
O3viii—Ba1—O3x134.89 (2)Ba1xxii—Mg2—Ba1xxiii102.785 (2)
O3ix—Ba1—O3x59.91 (2)O3xiii—Mg2—Ba1iii139.347 (17)
O3i—Ba1—O3xi85.141 (14)O3xiv—Mg2—Ba1iii40.653 (16)
O3ii—Ba1—O3xi116.53 (2)O3xv—Mg2—Ba1iii130.781 (17)
O3iii—Ba1—O3xi57.15 (2)O3xvi—Mg2—Ba1iii49.219 (17)
O3iv—Ba1—O3xi84.430 (13)O3xvii—Mg2—Ba1iii81.522 (17)
O3v—Ba1—O3xi176.440 (13)O3xviii—Mg2—Ba1iii98.478 (17)
O3vi—Ba1—O3xi43.91 (2)Ba1xix—Mg2—Ba1iii102.785 (3)
O3vii—Ba1—O3xi97.522 (14)Ba1xx—Mg2—Ba1iii77.215 (3)
O3viii—Ba1—O3xi59.91 (2)Ba1xxi—Mg2—Ba1iii102.785 (2)
O3ix—Ba1—O3xi122.25 (2)Ba1xxii—Mg2—Ba1iii77.215 (2)
O3x—Ba1—O3xi97.522 (14)Ba1xxiii—Mg2—Ba1iii180.0
O3i—Ba1—O3xii116.53 (2)C4xxiv—O3—Mg2xxv138.81 (5)
O3ii—Ba1—O3xii85.141 (14)C4xxiv—O3—Ba1iii101.07 (4)
O3iii—Ba1—O3xii84.430 (13)Mg2xxv—O3—Ba1iii110.72 (2)
O3iv—Ba1—O3xii57.15 (2)C4xxiv—O3—Ba1x87.35 (3)
O3v—Ba1—O3xii43.91 (2)Mg2xxv—O3—Ba1x100.54 (2)
O3vi—Ba1—O3xii176.440 (13)Ba1iii—O3—Ba1x116.53 (2)
O3vii—Ba1—O3xii59.91 (2)O3xxvi—C4—O3xxvii119.914 (5)
O3viii—Ba1—O3xii97.522 (14)O3xxvi—C4—O3xxviii119.914 (5)
O3ix—Ba1—O3xii97.522 (14)O3xxvii—C4—O3xxviii119.914 (5)
O3x—Ba1—O3xii122.25 (2)O3xxvi—C4—Ba1xxii148.89 (6)
O3xi—Ba1—O3xii134.89 (2)O3xxvii—C4—Ba1xxii69.76 (3)
O3xiii—Mg2—O3xiv180.00 (5)O3xxviii—C4—Ba1xxii56.47 (3)
O3xiii—Mg2—O3xv86.90 (2)O3xxvi—C4—Ba1xx56.47 (3)
O3xiv—Mg2—O3xv93.10 (2)O3xxvii—C4—Ba1xx148.89 (6)
O3xiii—Mg2—O3xvi93.10 (2)O3xxviii—C4—Ba1xx69.76 (3)
O3xiv—Mg2—O3xvi86.90 (2)Ba1xxii—C4—Ba1xx99.102 (17)
O3xv—Mg2—O3xvi180.00 (4)O3xxvi—C4—Ba1iii69.76 (3)
O3xiii—Mg2—O3xvii86.90 (2)O3xxvii—C4—Ba1iii56.47 (3)
O3xiv—Mg2—O3xvii93.10 (2)O3xxviii—C4—Ba1iii148.89 (6)
O3xv—Mg2—O3xvii86.90 (2)Ba1xxii—C4—Ba1iii99.101 (17)
O3xvi—Mg2—O3xvii93.10 (2)Ba1xx—C4—Ba1iii99.101 (17)
O3xiii—Mg2—O3xviii93.10 (2)
Symmetry codes: (i) x+y2/3, y1/3, z+1/6; (ii) y1/3, x+y2/3, z+1/3; (iii) x1/3, y+1/3, z+1/3; (iv) y+1/3, x1/3, z+1/6; (v) x+1/3, xy+2/3, z+1/6; (vi) xy+2/3, x+1/3, z+1/3; (vii) xy+2/3, x2/3, z+1/3; (viii) x2/3, xy+2/3, z+1/6; (ix) y+4/3, x+2/3, z+1/6; (x) x+2/3, y+4/3, z+1/3; (xi) y4/3, x+y2/3, z+1/3; (xii) x+y2/3, y4/3, z+1/6; (xiii) x+y1/3, y2/3, z1/6; (xiv) xy+1/3, y+2/3, z+1/6; (xv) x1/3, xy+1/3, z1/6; (xvi) x+1/3, x+y1/3, z+1/6; (xvii) y+2/3, x+1/3, z1/6; (xviii) y2/3, x1/3, z+1/6; (xix) x2/3, y1/3, z1/3; (xx) x+2/3, y+1/3, z+1/3; (xxi) x+1/3, y+2/3, z1/3; (xxii) x1/3, y2/3, z+1/3; (xxiii) x+1/3, y1/3, z1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, z+1/6; (xxvi) y+1, xy+1, z; (xxvii) x+y1, x, z; (xxviii) x, y1, z.
(norse_200) top
Crystal data top
C6Ba3Mg3O18Dx = 3.850 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 9363 reflections
a = 5.0113 (1) Åθ = 1.5–45°
c = 33.5158 (10) ŵ = 8.26 mm1
V = 728.92 (4) Å3T = 200 K
Z = 2Prismatic
F(000) = 7680.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.030
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.6°, θmin = 3.7°
Tmin = 0.7, Tmax = 0.8h = 109
9363 measured reflectionsk = 910
697 independent reflectionsl = 3465
515 reflections with I > 2σ(I)
Refinement top
Refinement on F217 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.010 w = 1/[σ2(Fo2) + (0.0117P)2]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.020(Δ/σ)max < 0.001
S = 0.95Δρmax = 0.54 e Å3
697 reflectionsΔρmin = 0.58 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.25000.00759 (2)
Mg20.00000.00000.00000.00639 (7)
O30.11331 (15)0.82114 (14)0.12927 (2)0.01391 (11)
C40.00000.00000.13034 (3)0.00705 (11)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.00656 (2)0.00656 (2)0.00965 (3)0.00328 (1)0.0000.000
Mg20.00542 (10)0.00542 (10)0.00834 (16)0.00271 (5)0.0000.000
O30.0180 (3)0.0150 (3)0.01585 (18)0.0135 (3)0.00596 (18)0.00361 (18)
C40.00680 (16)0.00680 (16)0.0076 (2)0.00340 (8)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.8079 (6)Mg2—O3xviii2.0589 (6)
Ba1—O3ii2.8079 (6)Mg2—Ba1xix4.0215 (1)
Ba1—O3iii2.8079 (6)Mg2—Ba1xx4.0215 (1)
Ba1—O3iv2.8079 (6)Mg2—Ba1xxi4.0215 (1)
Ba1—O3v2.8079 (6)Mg2—Ba1xxii4.0215 (1)
Ba1—O3vi2.8079 (6)Mg2—Ba1xxiii4.0215 (1)
Ba1—O3vii3.0872 (7)Mg2—Ba1i4.0215 (1)
Ba1—O3viii3.0872 (6)O3—C4xxiv1.2791 (6)
Ba1—O3ix3.0872 (6)O3—Mg2xxv2.0589 (6)
Ba1—O3x3.0872 (7)O3—Ba1i2.8079 (6)
Ba1—O3xi3.0872 (6)O3—Ba1x3.0872 (6)
Ba1—O3xii3.0872 (6)C4—O3xxvi1.2791 (6)
Mg2—O3xiii2.0589 (6)C4—O3xxvii1.2791 (6)
Mg2—O3xiv2.0589 (6)C4—O3xxviii1.2791 (6)
Mg2—O3xv2.0589 (6)C4—Ba1xxii3.2943 (4)
Mg2—O3xvi2.0589 (6)C4—Ba1xx3.2943 (4)
Mg2—O3xvii2.0589 (6)C4—Ba1i3.2944 (4)
O3i—Ba1—O3ii137.57 (2)O3xiv—Mg2—O3xviii86.80 (2)
O3i—Ba1—O3iii123.67 (2)O3xv—Mg2—O3xviii93.20 (2)
O3ii—Ba1—O3iii92.811 (18)O3xvi—Mg2—O3xviii86.80 (2)
O3i—Ba1—O3iv67.01 (3)O3xvii—Mg2—O3xviii180.00 (4)
O3ii—Ba1—O3iv92.811 (18)O3xiii—Mg2—Ba1xix98.346 (17)
O3iii—Ba1—O3iv92.811 (18)O3xiv—Mg2—Ba1xix81.654 (17)
O3i—Ba1—O3v92.811 (18)O3xv—Mg2—Ba1xix40.848 (17)
O3ii—Ba1—O3v67.01 (3)O3xvi—Mg2—Ba1xix139.152 (17)
O3iii—Ba1—O3v137.57 (3)O3xvii—Mg2—Ba1xix48.928 (18)
O3iv—Ba1—O3v123.67 (2)O3xviii—Mg2—Ba1xix131.072 (18)
O3i—Ba1—O3vi92.811 (18)O3xiii—Mg2—Ba1xx81.654 (17)
O3ii—Ba1—O3vi123.67 (2)O3xiv—Mg2—Ba1xx98.346 (17)
O3iii—Ba1—O3vi67.01 (3)O3xv—Mg2—Ba1xx139.152 (17)
O3iv—Ba1—O3vi137.57 (2)O3xvi—Mg2—Ba1xx40.848 (17)
O3v—Ba1—O3vi92.811 (18)O3xvii—Mg2—Ba1xx131.072 (18)
O3i—Ba1—O3vii176.633 (14)O3xviii—Mg2—Ba1xx48.928 (18)
O3ii—Ba1—O3vii43.81 (2)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii57.13 (2)O3xiii—Mg2—Ba1xxi48.926 (18)
O3iv—Ba1—O3vii116.36 (2)O3xiv—Mg2—Ba1xxi131.074 (18)
O3v—Ba1—O3vii85.233 (14)O3xv—Mg2—Ba1xxi98.346 (17)
O3vi—Ba1—O3vii84.558 (13)O3xvi—Mg2—Ba1xxi81.654 (17)
O3i—Ba1—O3viii43.81 (2)O3xvii—Mg2—Ba1xxi40.850 (17)
O3ii—Ba1—O3viii176.633 (13)O3xviii—Mg2—Ba1xxi139.150 (17)
O3iii—Ba1—O3viii84.558 (13)Ba1xix—Mg2—Ba1xxi77.081 (2)
O3iv—Ba1—O3viii85.233 (14)Ba1xx—Mg2—Ba1xxi102.919 (2)
O3v—Ba1—O3viii116.36 (2)O3xiii—Mg2—Ba1xxii131.074 (18)
O3vi—Ba1—O3viii57.13 (2)O3xiv—Mg2—Ba1xxii48.926 (18)
O3vii—Ba1—O3viii135.05 (2)O3xv—Mg2—Ba1xxii81.654 (17)
O3i—Ba1—O3ix57.13 (2)O3xvi—Mg2—Ba1xxii98.346 (17)
O3ii—Ba1—O3ix85.233 (14)O3xvii—Mg2—Ba1xxii139.150 (17)
O3iii—Ba1—O3ix176.633 (13)O3xviii—Mg2—Ba1xxii40.850 (17)
O3iv—Ba1—O3ix84.558 (13)Ba1xix—Mg2—Ba1xxii102.919 (2)
O3v—Ba1—O3ix43.81 (2)Ba1xx—Mg2—Ba1xxii77.081 (2)
O3vi—Ba1—O3ix116.36 (2)Ba1xxi—Mg2—Ba1xxii180.0
O3vii—Ba1—O3ix122.30 (2)O3xiii—Mg2—Ba1xxiii40.850 (17)
O3viii—Ba1—O3ix97.293 (14)O3xiv—Mg2—Ba1xxiii139.150 (17)
O3i—Ba1—O3x116.36 (2)O3xv—Mg2—Ba1xxiii48.928 (18)
O3ii—Ba1—O3x84.558 (13)O3xvi—Mg2—Ba1xxiii131.072 (18)
O3iii—Ba1—O3x85.233 (14)O3xvii—Mg2—Ba1xxiii98.348 (17)
O3iv—Ba1—O3x176.633 (14)O3xviii—Mg2—Ba1xxiii81.652 (17)
O3v—Ba1—O3x57.13 (2)Ba1xix—Mg2—Ba1xxiii77.081 (1)
O3vi—Ba1—O3x43.81 (2)Ba1xx—Mg2—Ba1xxiii102.919 (1)
O3vii—Ba1—O3x60.27 (2)Ba1xxi—Mg2—Ba1xxiii77.081 (2)
O3viii—Ba1—O3x97.293 (14)Ba1xxii—Mg2—Ba1xxiii102.919 (2)
O3ix—Ba1—O3x97.293 (14)O3xiii—Mg2—Ba1i139.150 (17)
O3i—Ba1—O3xi85.233 (14)O3xiv—Mg2—Ba1i40.850 (17)
O3ii—Ba1—O3xi57.13 (2)O3xv—Mg2—Ba1i131.072 (18)
O3iii—Ba1—O3xi116.36 (2)O3xvi—Mg2—Ba1i48.928 (18)
O3iv—Ba1—O3xi43.81 (2)O3xvii—Mg2—Ba1i81.652 (17)
O3v—Ba1—O3xi84.558 (13)O3xviii—Mg2—Ba1i98.348 (17)
O3vi—Ba1—O3xi176.633 (13)Ba1xix—Mg2—Ba1i102.919 (1)
O3vii—Ba1—O3xi97.293 (14)Ba1xx—Mg2—Ba1i77.081 (1)
O3viii—Ba1—O3xi122.30 (2)Ba1xxi—Mg2—Ba1i102.919 (2)
O3ix—Ba1—O3xi60.27 (2)Ba1xxii—Mg2—Ba1i77.081 (2)
O3x—Ba1—O3xi135.05 (2)Ba1xxiii—Mg2—Ba1i180.0
O3i—Ba1—O3xii84.558 (13)C4xxiv—O3—Mg2xxv139.05 (6)
O3ii—Ba1—O3xii116.36 (2)C4xxiv—O3—Ba1i100.69 (4)
O3iii—Ba1—O3xii43.81 (2)Mg2xxv—O3—Ba1i110.49 (2)
O3iv—Ba1—O3xii57.13 (2)C4xxiv—O3—Ba1x87.72 (4)
O3v—Ba1—O3xii176.633 (13)Mg2xxv—O3—Ba1x100.89 (2)
O3vi—Ba1—O3xii85.233 (14)Ba1i—O3—Ba1x116.36 (2)
O3vii—Ba1—O3xii97.293 (14)O3xxvi—C4—O3xxvii119.923 (5)
O3viii—Ba1—O3xii60.27 (2)O3xxvi—C4—O3xxviii119.923 (5)
O3ix—Ba1—O3xii135.05 (2)O3xxvii—C4—O3xxviii119.921 (5)
O3x—Ba1—O3xii122.30 (2)O3xxvi—C4—Ba1xxii56.88 (3)
O3xi—Ba1—O3xii97.293 (14)O3xxvii—C4—Ba1xxii149.01 (6)
O3xiii—Mg2—O3xiv180.00 (5)O3xxviii—C4—Ba1xxii69.45 (3)
O3xiii—Mg2—O3xv86.80 (2)O3xxvi—C4—Ba1xx69.45 (3)
O3xiv—Mg2—O3xv93.20 (2)O3xxvii—C4—Ba1xx56.88 (3)
O3xiii—Mg2—O3xvi93.20 (2)O3xxviii—C4—Ba1xx149.01 (6)
O3xiv—Mg2—O3xvi86.80 (2)Ba1xxii—C4—Ba1xx99.033 (17)
O3xv—Mg2—O3xvi180.00 (5)O3xxvi—C4—Ba1i149.01 (6)
O3xiii—Mg2—O3xvii86.80 (2)O3xxvii—C4—Ba1i69.45 (3)
O3xiv—Mg2—O3xvii93.20 (2)O3xxviii—C4—Ba1i56.88 (3)
O3xv—Mg2—O3xvii86.80 (2)Ba1xxii—C4—Ba1i99.032 (17)
O3xvi—Mg2—O3xvii93.20 (2)Ba1xx—C4—Ba1i99.032 (17)
O3xiii—Mg2—O3xviii93.20 (2)
Symmetry codes: (i) x1/3, y+1/3, z+1/3; (ii) x+y2/3, y1/3, z+1/6; (iii) x+1/3, xy+2/3, z+1/6; (iv) y+1/3, x1/3, z+1/6; (v) xy+2/3, x+1/3, z+1/3; (vi) y1/3, x+y2/3, z+1/3; (vii) y+4/3, x+2/3, z+1/6; (viii) xy+2/3, x2/3, z+1/3; (ix) y4/3, x+y2/3, z+1/3; (x) x+2/3, y+4/3, z+1/3; (xi) x2/3, xy+2/3, z+1/6; (xii) x+y2/3, y4/3, z+1/6; (xiii) x+y1/3, y2/3, z1/6; (xiv) xy+1/3, y+2/3, z+1/6; (xv) x1/3, xy+1/3, z1/6; (xvi) x+1/3, x+y1/3, z+1/6; (xvii) y+2/3, x+1/3, z1/6; (xviii) y2/3, x1/3, z+1/6; (xix) x2/3, y1/3, z1/3; (xx) x+2/3, y+1/3, z+1/3; (xxi) x+1/3, y+2/3, z1/3; (xxii) x1/3, y2/3, z+1/3; (xxiii) x+1/3, y1/3, z1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, z+1/6; (xxvi) x, y1, z; (xxvii) y+1, xy+1, z; (xxviii) x+y1, x, z.
(norse_250) top
Crystal data top
C6Ba3Mg3O18Dx = 3.851 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 9496 reflections
a = 5.0135 (1) Åθ = 1.5–45°
c = 33.4784 (9) ŵ = 8.26 mm1
V = 728.75 (4) Å3T = 250 K
Z = 2Prismatic
F(000) = 7680.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.031
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.6°, θmin = 3.7°
Tmin = 0.7, Tmax = 0.8h = 109
9496 measured reflectionsk = 910
697 independent reflectionsl = 3465
488 reflections with I > 2σ(I)
Refinement top
Refinement on F217 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.010 w = 1/[σ2(Fo2) + (0.0112P)2]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.021(Δ/σ)max < 0.001
S = 0.95Δρmax = 0.43 e Å3
697 reflectionsΔρmin = 0.60 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.25000.00913 (2)
Mg20.00000.00000.00000.00736 (7)
O30.11588 (17)0.82345 (17)0.12923 (2)0.01653 (13)
C40.00000.00000.13039 (3)0.00794 (11)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.00793 (2)0.00793 (2)0.01153 (3)0.00396 (1)0.0000.000
Mg20.00632 (10)0.00632 (10)0.00942 (17)0.00316 (5)0.0000.000
O30.0219 (4)0.0177 (3)0.0185 (2)0.0163 (3)0.0070 (2)0.0041 (2)
C40.00766 (17)0.00766 (17)0.0085 (3)0.00383 (9)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.8171 (7)Mg2—O3xviii2.0578 (6)
Ba1—O3ii2.8171 (7)Mg2—Ba1xix4.0202 (1)
Ba1—O3iii2.8172 (7)Mg2—Ba1xx4.0202 (1)
Ba1—O3iv2.8172 (7)Mg2—Ba1xxi4.0202 (1)
Ba1—O3v2.8172 (7)Mg2—Ba1xxii4.0202 (1)
Ba1—O3vi2.8172 (7)Mg2—Ba1xxiii4.0202 (1)
Ba1—O3vii3.0759 (8)Mg2—Ba1iii4.0202 (1)
Ba1—O3viii3.0759 (8)O3—C4xxiv1.2793 (6)
Ba1—O3ix3.0759 (8)O3—Mg2xxv2.0578 (6)
Ba1—O3x3.0759 (8)O3—Ba1iii2.8172 (7)
Ba1—O3xi3.0759 (8)O3—Ba1x3.0759 (8)
Ba1—O3xii3.0759 (8)C4—O3xxvi1.2793 (6)
Mg2—O3xiii2.0577 (6)C4—O3xxvii1.2793 (6)
Mg2—O3xiv2.0577 (6)C4—O3xxviii1.2793 (6)
Mg2—O3xv2.0577 (6)C4—Ba1xxii3.2955 (4)
Mg2—O3xvi2.0577 (6)C4—Ba1xx3.2955 (4)
Mg2—O3xvii2.0578 (6)C4—Ba1iii3.2955 (4)
O3i—Ba1—O3ii123.60 (2)O3xiv—Mg2—O3xviii86.76 (3)
O3i—Ba1—O3iii137.39 (3)O3xv—Mg2—O3xviii93.24 (3)
O3ii—Ba1—O3iii93.09 (2)O3xvi—Mg2—O3xviii86.76 (3)
O3i—Ba1—O3iv93.09 (2)O3xvii—Mg2—O3xviii180.00 (4)
O3ii—Ba1—O3iv137.39 (3)O3xiii—Mg2—Ba1xix98.387 (18)
O3iii—Ba1—O3iv66.60 (3)O3xiv—Mg2—Ba1xix81.613 (18)
O3i—Ba1—O3v93.09 (2)O3xv—Mg2—Ba1xix41.14 (2)
O3ii—Ba1—O3v66.60 (3)O3xvi—Mg2—Ba1xix138.86 (2)
O3iii—Ba1—O3v123.60 (2)O3xvii—Mg2—Ba1xix48.63 (2)
O3iv—Ba1—O3v93.09 (2)O3xviii—Mg2—Ba1xix131.37 (2)
O3i—Ba1—O3vi66.60 (3)O3xiii—Mg2—Ba1xx81.613 (18)
O3ii—Ba1—O3vi93.09 (2)O3xiv—Mg2—Ba1xx98.387 (18)
O3iii—Ba1—O3vi93.09 (2)O3xv—Mg2—Ba1xx138.86 (2)
O3iv—Ba1—O3vi123.60 (2)O3xvi—Mg2—Ba1xx41.14 (2)
O3v—Ba1—O3vi137.39 (3)O3xvii—Mg2—Ba1xx131.37 (2)
O3i—Ba1—O3vii176.888 (16)O3xviii—Mg2—Ba1xx48.63 (2)
O3ii—Ba1—O3vii57.13 (2)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii43.88 (2)O3xiii—Mg2—Ba1xxi48.63 (2)
O3iv—Ba1—O3vii85.108 (15)O3xiv—Mg2—Ba1xxi131.37 (2)
O3v—Ba1—O3vii84.487 (14)O3xv—Mg2—Ba1xxi98.387 (18)
O3vi—Ba1—O3vii116.52 (2)O3xvi—Mg2—Ba1xxi81.613 (18)
O3i—Ba1—O3viii57.13 (2)O3xvii—Mg2—Ba1xxi41.15 (2)
O3ii—Ba1—O3viii176.888 (16)O3xviii—Mg2—Ba1xxi138.85 (2)
O3iii—Ba1—O3viii85.108 (15)Ba1xix—Mg2—Ba1xxi77.150 (1)
O3iv—Ba1—O3viii43.88 (2)Ba1xx—Mg2—Ba1xxi102.850 (2)
O3v—Ba1—O3viii116.52 (2)O3xiii—Mg2—Ba1xxii131.37 (2)
O3vi—Ba1—O3viii84.487 (14)O3xiv—Mg2—Ba1xxii48.63 (2)
O3vii—Ba1—O3viii122.34 (2)O3xv—Mg2—Ba1xxii81.613 (18)
O3i—Ba1—O3ix43.88 (2)O3xvi—Mg2—Ba1xxii98.387 (18)
O3ii—Ba1—O3ix84.486 (14)O3xvii—Mg2—Ba1xxii138.85 (2)
O3iii—Ba1—O3ix176.888 (17)O3xviii—Mg2—Ba1xxii41.15 (2)
O3iv—Ba1—O3ix116.52 (2)Ba1xix—Mg2—Ba1xxii102.850 (2)
O3v—Ba1—O3ix57.12 (2)Ba1xx—Mg2—Ba1xxii77.150 (1)
O3vi—Ba1—O3ix85.108 (15)Ba1xxi—Mg2—Ba1xxii180.0
O3vii—Ba1—O3ix135.06 (2)O3xiii—Mg2—Ba1xxiii41.15 (2)
O3viii—Ba1—O3ix97.226 (16)O3xiv—Mg2—Ba1xxiii138.85 (2)
O3i—Ba1—O3x84.486 (14)O3xv—Mg2—Ba1xxiii48.63 (2)
O3ii—Ba1—O3x43.88 (2)O3xvi—Mg2—Ba1xxiii131.37 (2)
O3iii—Ba1—O3x116.52 (2)O3xvii—Mg2—Ba1xxiii98.387 (18)
O3iv—Ba1—O3x176.888 (17)O3xviii—Mg2—Ba1xxiii81.613 (18)
O3v—Ba1—O3x85.108 (15)Ba1xix—Mg2—Ba1xxiii77.149 (1)
O3vi—Ba1—O3x57.12 (2)Ba1xx—Mg2—Ba1xxiii102.851 (1)
O3vii—Ba1—O3x97.226 (16)Ba1xxi—Mg2—Ba1xxiii77.149 (1)
O3viii—Ba1—O3x135.06 (2)Ba1xxii—Mg2—Ba1xxiii102.851 (2)
O3ix—Ba1—O3x60.37 (3)O3xiii—Mg2—Ba1iii138.85 (2)
O3i—Ba1—O3xi85.108 (15)O3xiv—Mg2—Ba1iii41.15 (2)
O3ii—Ba1—O3xi116.52 (2)O3xv—Mg2—Ba1iii131.37 (2)
O3iii—Ba1—O3xi57.12 (2)O3xvi—Mg2—Ba1iii48.63 (2)
O3iv—Ba1—O3xi84.487 (14)O3xvii—Mg2—Ba1iii81.613 (18)
O3v—Ba1—O3xi176.888 (16)O3xviii—Mg2—Ba1iii98.387 (18)
O3vi—Ba1—O3xi43.88 (2)Ba1xix—Mg2—Ba1iii102.851 (1)
O3vii—Ba1—O3xi97.226 (16)Ba1xx—Mg2—Ba1iii77.149 (1)
O3viii—Ba1—O3xi60.37 (2)Ba1xxi—Mg2—Ba1iii102.851 (2)
O3ix—Ba1—O3xi122.34 (2)Ba1xxii—Mg2—Ba1iii77.149 (1)
O3x—Ba1—O3xi97.226 (16)Ba1xxiii—Mg2—Ba1iii180.0
O3i—Ba1—O3xii116.52 (2)C4xxiv—O3—Mg2xxv139.14 (6)
O3ii—Ba1—O3xii85.108 (15)C4xxiv—O3—Ba1iii100.29 (4)
O3iii—Ba1—O3xii84.487 (14)Mg2xxv—O3—Ba1iii110.13 (3)
O3iv—Ba1—O3xii57.12 (2)C4xxiv—O3—Ba1x88.27 (4)
O3v—Ba1—O3xii43.88 (2)Mg2xxv—O3—Ba1x101.23 (3)
O3vi—Ba1—O3xii176.888 (16)Ba1iii—O3—Ba1x116.52 (2)
O3vii—Ba1—O3xii60.37 (2)O3xxvi—C4—O3xxvii119.908 (6)
O3viii—Ba1—O3xii97.226 (16)O3xxvi—C4—O3xxviii119.908 (6)
O3ix—Ba1—O3xii97.226 (16)O3xxvii—C4—O3xxviii119.908 (5)
O3x—Ba1—O3xii122.34 (2)O3xxvi—C4—Ba1xxii149.00 (6)
O3xi—Ba1—O3xii135.06 (2)O3xxvii—C4—Ba1xxii68.90 (4)
O3xiii—Mg2—O3xiv180.00 (3)O3xxviii—C4—Ba1xxii57.26 (4)
O3xiii—Mg2—O3xv86.76 (3)O3xxvi—C4—Ba1xx57.26 (4)
O3xiv—Mg2—O3xv93.24 (3)O3xxvii—C4—Ba1xx149.00 (6)
O3xiii—Mg2—O3xvi93.24 (3)O3xxviii—C4—Ba1xx68.90 (4)
O3xiv—Mg2—O3xvi86.76 (3)Ba1xxii—C4—Ba1xx99.046 (17)
O3xv—Mg2—O3xvi180.00 (4)O3xxvi—C4—Ba1iii68.90 (4)
O3xiii—Mg2—O3xvii86.76 (3)O3xxvii—C4—Ba1iii57.26 (4)
O3xiv—Mg2—O3xvii93.24 (3)O3xxviii—C4—Ba1iii149.00 (6)
O3xv—Mg2—O3xvii86.76 (3)Ba1xxii—C4—Ba1iii99.045 (17)
O3xvi—Mg2—O3xvii93.24 (3)Ba1xx—C4—Ba1iii99.045 (17)
O3xiii—Mg2—O3xviii93.24 (3)
Symmetry codes: (i) x+y2/3, y1/3, z+1/6; (ii) y1/3, x+y2/3, z+1/3; (iii) x1/3, y+1/3, z+1/3; (iv) y+1/3, x1/3, z+1/6; (v) x+1/3, xy+2/3, z+1/6; (vi) xy+2/3, x+1/3, z+1/3; (vii) xy+2/3, x2/3, z+1/3; (viii) x2/3, xy+2/3, z+1/6; (ix) y+4/3, x+2/3, z+1/6; (x) x+2/3, y+4/3, z+1/3; (xi) y4/3, x+y2/3, z+1/3; (xii) x+y2/3, y4/3, z+1/6; (xiii) x+y1/3, y2/3, z1/6; (xiv) xy+1/3, y+2/3, z+1/6; (xv) x1/3, xy+1/3, z1/6; (xvi) x+1/3, x+y1/3, z+1/6; (xvii) y+2/3, x+1/3, z1/6; (xviii) y2/3, x1/3, z+1/6; (xix) x2/3, y1/3, z1/3; (xx) x+2/3, y+1/3, z+1/3; (xxi) x+1/3, y+2/3, z1/3; (xxii) x1/3, y2/3, z+1/3; (xxiii) x+1/3, y1/3, z1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, z+1/6; (xxvi) y+1, xy+1, z; (xxvii) x+y1, x, z; (xxviii) x, y1, z.
(norse_280) top
Crystal data top
C6Ba3Mg3O18Dx = 3.845 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 9450 reflections
a = 5.0161 (1) Åθ = 1.5–40°
c = 33.4952 (8) ŵ = 8.25 mm1
V = 729.87 (3) Å3T = 280 K
Z = 2Prismatic
F(000) = 7680.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.029
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.6°, θmin = 3.7°
Tmin = 0.7, Tmax = 0.8h = 109
9450 measured reflectionsk = 910
699 independent reflectionsl = 3666
507 reflections with I > 2σ(I)
Refinement top
Refinement on F217 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.010 w = 1/[σ2(Fo2) + (0.0127P)2]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.023(Δ/σ)max < 0.001
S = 1.03Δρmax = 0.53 e Å3
699 reflectionsΔρmin = 0.40 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.25000.00992 (2)
Mg20.00000.00000.00000.00804 (7)
O30.11770 (16)0.82531 (16)0.12921 (2)0.01808 (12)
C40.00000.00000.13039 (3)0.00870 (11)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.00867 (2)0.00867 (2)0.01241 (3)0.00434 (1)0.0000.000
Mg20.00690 (11)0.00690 (11)0.01031 (17)0.00345 (5)0.0000.000
O30.0236 (3)0.0198 (3)0.0202 (2)0.0179 (3)0.0075 (2)0.0043 (2)
C40.00849 (17)0.00849 (17)0.0091 (3)0.00424 (9)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.8261 (7)Mg2—O3xviii2.0586 (6)
Ba1—O3ii2.8261 (7)Mg2—Ba1xix4.0223 (1)
Ba1—O3iii2.8261 (7)Mg2—Ba1xx4.0223 (1)
Ba1—O3iv2.8261 (7)Mg2—Ba1xxi4.0223 (1)
Ba1—O3v2.8261 (7)Mg2—Ba1xxii4.0223 (1)
Ba1—O3vi2.8261 (7)Mg2—Ba1xxiii4.0223 (1)
Ba1—O3vii3.0693 (7)Mg2—Ba1iii4.0223 (1)
Ba1—O3viii3.0693 (7)O3—C4xxiv1.2788 (6)
Ba1—O3ix3.0693 (8)O3—Mg2xxv2.0585 (6)
Ba1—O3x3.0693 (8)O3—Ba1iii2.8261 (7)
Ba1—O3xi3.0693 (7)O3—Ba1x3.0693 (7)
Ba1—O3xii3.0693 (7)C4—O3xxvi1.2788 (6)
Mg2—O3xiii2.0586 (6)C4—O3xxvii1.2788 (6)
Mg2—O3xiv2.0586 (6)C4—O3xxviii1.2788 (6)
Mg2—O3xv2.0586 (6)C4—Ba1xxii3.2971 (4)
Mg2—O3xvi2.0586 (6)C4—Ba1xx3.2971 (4)
Mg2—O3xvii2.0586 (6)C4—Ba1iii3.2971 (4)
O3i—Ba1—O3ii123.55 (3)O3xiv—Mg2—O3xviii86.73 (3)
O3i—Ba1—O3iii137.32 (3)O3xv—Mg2—O3xviii93.27 (3)
O3ii—Ba1—O3iii93.24 (2)O3xvi—Mg2—O3xviii86.73 (3)
O3i—Ba1—O3iv93.24 (2)O3xvii—Mg2—O3xviii180.00 (4)
O3ii—Ba1—O3iv137.32 (3)O3xiii—Mg2—Ba1xix98.382 (19)
O3iii—Ba1—O3iv66.37 (3)O3xiv—Mg2—Ba1xix81.618 (19)
O3i—Ba1—O3v93.24 (2)O3xv—Mg2—Ba1xix41.363 (19)
O3ii—Ba1—O3v66.37 (3)O3xvi—Mg2—Ba1xix138.637 (19)
O3iii—Ba1—O3v123.55 (2)O3xvii—Mg2—Ba1xix48.40 (2)
O3iv—Ba1—O3v93.24 (2)O3xviii—Mg2—Ba1xix131.60 (2)
O3i—Ba1—O3vi66.37 (3)O3xiii—Mg2—Ba1xx81.618 (19)
O3ii—Ba1—O3vi93.24 (2)O3xiv—Mg2—Ba1xx98.382 (19)
O3iii—Ba1—O3vi93.24 (2)O3xv—Mg2—Ba1xx138.637 (19)
O3iv—Ba1—O3vi123.55 (2)O3xvi—Mg2—Ba1xx41.363 (19)
O3v—Ba1—O3vi137.32 (3)O3xvii—Mg2—Ba1xx131.60 (2)
O3i—Ba1—O3vii177.078 (15)O3xviii—Mg2—Ba1xx48.40 (2)
O3ii—Ba1—O3vii57.13 (2)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii43.87 (2)O3xiii—Mg2—Ba1xxi48.40 (2)
O3iv—Ba1—O3vii85.069 (15)O3xiv—Mg2—Ba1xxi131.60 (2)
O3v—Ba1—O3vii84.485 (15)O3xv—Mg2—Ba1xxi98.382 (19)
O3vi—Ba1—O3vii116.55 (2)O3xvi—Mg2—Ba1xxi81.618 (19)
O3i—Ba1—O3viii57.13 (2)O3xvii—Mg2—Ba1xxi41.364 (19)
O3ii—Ba1—O3viii177.078 (15)O3xviii—Mg2—Ba1xxi138.636 (19)
O3iii—Ba1—O3viii85.069 (15)Ba1xix—Mg2—Ba1xxi77.150 (1)
O3iv—Ba1—O3viii43.87 (2)Ba1xx—Mg2—Ba1xxi102.850 (1)
O3v—Ba1—O3viii116.55 (2)O3xiii—Mg2—Ba1xxii131.60 (2)
O3vi—Ba1—O3viii84.485 (15)O3xiv—Mg2—Ba1xxii48.40 (2)
O3vii—Ba1—O3viii122.36 (2)O3xv—Mg2—Ba1xxii81.618 (19)
O3i—Ba1—O3ix43.87 (2)O3xvi—Mg2—Ba1xxii98.382 (19)
O3ii—Ba1—O3ix84.485 (15)O3xvii—Mg2—Ba1xxii138.636 (19)
O3iii—Ba1—O3ix177.078 (16)O3xviii—Mg2—Ba1xxii41.364 (19)
O3iv—Ba1—O3ix116.55 (2)Ba1xix—Mg2—Ba1xxii102.850 (1)
O3v—Ba1—O3ix57.13 (2)Ba1xx—Mg2—Ba1xxii77.150 (1)
O3vi—Ba1—O3ix85.070 (15)Ba1xxi—Mg2—Ba1xxii180.0
O3vii—Ba1—O3ix135.13 (2)O3xiii—Mg2—Ba1xxiii41.364 (19)
O3viii—Ba1—O3ix97.125 (16)O3xiv—Mg2—Ba1xxiii138.636 (19)
O3i—Ba1—O3x84.485 (15)O3xv—Mg2—Ba1xxiii48.40 (2)
O3ii—Ba1—O3x43.87 (2)O3xvi—Mg2—Ba1xxiii131.60 (2)
O3iii—Ba1—O3x116.55 (2)O3xvii—Mg2—Ba1xxiii98.383 (19)
O3iv—Ba1—O3x177.078 (16)O3xviii—Mg2—Ba1xxiii81.617 (19)
O3v—Ba1—O3x85.070 (15)Ba1xix—Mg2—Ba1xxiii77.150 (1)
O3vi—Ba1—O3x57.13 (2)Ba1xx—Mg2—Ba1xxiii102.850 (2)
O3vii—Ba1—O3x97.125 (16)Ba1xxi—Mg2—Ba1xxiii77.150 (1)
O3viii—Ba1—O3x135.13 (2)Ba1xxii—Mg2—Ba1xxiii102.850 (1)
O3ix—Ba1—O3x60.53 (3)O3xiii—Mg2—Ba1iii138.636 (19)
O3i—Ba1—O3xi85.070 (15)O3xiv—Mg2—Ba1iii41.364 (19)
O3ii—Ba1—O3xi116.55 (2)O3xv—Mg2—Ba1iii131.60 (2)
O3iii—Ba1—O3xi57.13 (2)O3xvi—Mg2—Ba1iii48.40 (2)
O3iv—Ba1—O3xi84.486 (15)O3xvii—Mg2—Ba1iii81.617 (19)
O3v—Ba1—O3xi177.078 (15)O3xviii—Mg2—Ba1iii98.383 (19)
O3vi—Ba1—O3xi43.87 (2)Ba1xix—Mg2—Ba1iii102.850 (2)
O3vii—Ba1—O3xi97.125 (16)Ba1xx—Mg2—Ba1iii77.150 (1)
O3viii—Ba1—O3xi60.53 (3)Ba1xxi—Mg2—Ba1iii102.850 (1)
O3ix—Ba1—O3xi122.36 (2)Ba1xxii—Mg2—Ba1iii77.150 (1)
O3x—Ba1—O3xi97.125 (16)Ba1xxiii—Mg2—Ba1iii180.0
O3i—Ba1—O3xii116.55 (2)C4xxiv—O3—Mg2xxv139.29 (6)
O3ii—Ba1—O3xii85.070 (15)C4xxiv—O3—Ba1iii99.95 (4)
O3iii—Ba1—O3xii84.486 (15)Mg2xxv—O3—Ba1iii109.86 (3)
O3iv—Ba1—O3xii57.13 (2)C4xxiv—O3—Ba1x88.65 (4)
O3v—Ba1—O3xii43.87 (2)Mg2xxv—O3—Ba1x101.50 (3)
O3vi—Ba1—O3xii177.078 (15)Ba1iii—O3—Ba1x116.55 (2)
O3vii—Ba1—O3xii60.53 (3)O3xxvi—C4—O3xxvii119.906 (6)
O3viii—Ba1—O3xii97.125 (16)O3xxvi—C4—O3xxviii119.906 (6)
O3ix—Ba1—O3xii97.125 (16)O3xxvii—C4—O3xxviii119.906 (6)
O3x—Ba1—O3xii122.36 (2)O3xxvi—C4—Ba1xxii149.06 (6)
O3xi—Ba1—O3xii135.13 (2)O3xxvii—C4—Ba1xxii68.54 (4)
O3xiii—Mg2—O3xiv180.00 (7)O3xxviii—C4—Ba1xxii57.59 (4)
O3xiii—Mg2—O3xv86.73 (3)O3xxvi—C4—Ba1xx57.59 (4)
O3xiv—Mg2—O3xv93.27 (3)O3xxvii—C4—Ba1xx149.06 (6)
O3xiii—Mg2—O3xvi93.27 (3)O3xxviii—C4—Ba1xx68.54 (4)
O3xiv—Mg2—O3xvi86.73 (3)Ba1xxii—C4—Ba1xx99.049 (18)
O3xv—Mg2—O3xvi180.00 (5)O3xxvi—C4—Ba1iii68.54 (4)
O3xiii—Mg2—O3xvii86.73 (3)O3xxvii—C4—Ba1iii57.59 (4)
O3xiv—Mg2—O3xvii93.27 (3)O3xxviii—C4—Ba1iii149.06 (6)
O3xv—Mg2—O3xvii86.73 (3)Ba1xxii—C4—Ba1iii99.048 (18)
O3xvi—Mg2—O3xvii93.27 (3)Ba1xx—C4—Ba1iii99.048 (18)
O3xiii—Mg2—O3xviii93.27 (3)
Symmetry codes: (i) x+y2/3, y1/3, z+1/6; (ii) y1/3, x+y2/3, z+1/3; (iii) x1/3, y+1/3, z+1/3; (iv) y+1/3, x1/3, z+1/6; (v) x+1/3, xy+2/3, z+1/6; (vi) xy+2/3, x+1/3, z+1/3; (vii) xy+2/3, x2/3, z+1/3; (viii) x2/3, xy+2/3, z+1/6; (ix) y+4/3, x+2/3, z+1/6; (x) x+2/3, y+4/3, z+1/3; (xi) y4/3, x+y2/3, z+1/3; (xii) x+y2/3, y4/3, z+1/6; (xiii) x+y1/3, y2/3, z1/6; (xiv) xy+1/3, y+2/3, z+1/6; (xv) x1/3, xy+1/3, z1/6; (xvi) x+1/3, x+y1/3, z+1/6; (xvii) y+2/3, x+1/3, z1/6; (xviii) y2/3, x1/3, z+1/6; (xix) x2/3, y1/3, z1/3; (xx) x+2/3, y+1/3, z+1/3; (xxi) x+1/3, y+2/3, z1/3; (xxii) x1/3, y2/3, z+1/3; (xxiii) x+1/3, y1/3, z1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, z+1/6; (xxvi) y+1, xy+1, z; (xxvii) x+y1, x, z; (xxviii) x, y1, z.
(norse_299) top
Crystal data top
C6Ba3Mg3O18Dx = 3.843 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 9325 reflections
a = 5.0160 (1) Åθ = 1.5–45°
c = 33.5170 (13) ŵ = 8.24 mm1
V = 730.32 (4) Å3T = 299 K
Z = 2Prismatic
F(000) = 7680.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.031
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.5°, θmin = 3.7°
Tmin = 0.7, Tmax = 0.8h = 109
9325 measured reflectionsk = 910
698 independent reflectionsl = 3566
490 reflections with I > 2σ(I)
Refinement top
Refinement on F217 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.010 w = 1/[σ2(Fo2) + (0.0135P)2]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.023(Δ/σ)max < 0.001
S = 0.95Δρmax = 0.54 e Å3
698 reflectionsΔρmin = 0.52 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.25000.01061 (2)
Mg20.00000.00000.00000.00849 (7)
O30.11931 (18)0.82676 (17)0.12918 (2)0.01925 (13)
C40.00000.00000.13035 (3)0.00915 (11)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.00913 (2)0.00913 (2)0.01358 (3)0.00456 (1)0.0000.000
Mg20.00708 (11)0.00708 (11)0.01131 (17)0.00354 (5)0.0000.000
O30.0253 (4)0.0211 (3)0.0214 (2)0.0192 (3)0.0077 (3)0.0044 (2)
C40.00867 (17)0.00867 (17)0.0101 (3)0.00434 (9)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.8324 (7)Mg2—O3xviii2.0586 (6)
Ba1—O3ii2.8324 (7)Mg2—Ba1xix4.0235 (1)
Ba1—O3iii2.8324 (8)Mg2—Ba1xx4.0235 (1)
Ba1—O3iv2.8324 (8)Mg2—Ba1xxi4.0235 (1)
Ba1—O3v2.8324 (7)Mg2—Ba1xxii4.0235 (1)
Ba1—O3vi2.8324 (7)Mg2—Ba1xxiii4.0235 (1)
Ba1—O3vii3.0625 (8)Mg2—Ba1iii4.0235 (1)
Ba1—O3viii3.0625 (8)O3—C4xxiv1.2786 (6)
Ba1—O3ix3.0626 (8)O3—Mg2xxv2.0586 (6)
Ba1—O3x3.0626 (8)O3—Ba1iii2.8323 (7)
Ba1—O3xi3.0626 (8)O3—Ba1x3.0625 (8)
Ba1—O3xii3.0626 (8)C4—O3xxvi1.2786 (6)
Mg2—O3xiii2.0586 (6)C4—O3xxvii1.2786 (6)
Mg2—O3xiv2.0586 (6)C4—O3xxviii1.2786 (6)
Mg2—O3xv2.0586 (6)C4—Ba1xxii3.2969 (4)
Mg2—O3xvi2.0586 (6)C4—Ba1xx3.2969 (4)
Mg2—O3xvii2.0586 (6)C4—Ba1iii3.2970 (4)
O3i—Ba1—O3ii123.54 (3)O3xiv—Mg2—O3xviii86.64 (3)
O3i—Ba1—O3iii137.22 (3)O3xv—Mg2—O3xviii93.36 (3)
O3ii—Ba1—O3iii93.36 (2)O3xvi—Mg2—O3xviii86.64 (3)
O3i—Ba1—O3iv93.36 (2)O3xvii—Mg2—O3xviii180.00 (4)
O3ii—Ba1—O3iv137.22 (3)O3xiii—Mg2—Ba1xix98.311 (19)
O3iii—Ba1—O3iv66.20 (3)O3xiv—Mg2—Ba1xix81.689 (19)
O3i—Ba1—O3v93.36 (2)O3xv—Mg2—Ba1xix41.52 (2)
O3ii—Ba1—O3v66.20 (3)O3xvi—Mg2—Ba1xix138.48 (2)
O3iii—Ba1—O3v123.54 (3)O3xvii—Mg2—Ba1xix48.18 (2)
O3iv—Ba1—O3v93.36 (2)O3xviii—Mg2—Ba1xix131.82 (2)
O3i—Ba1—O3vi66.20 (3)O3xiii—Mg2—Ba1xx81.689 (19)
O3ii—Ba1—O3vi93.36 (2)O3xiv—Mg2—Ba1xx98.311 (19)
O3iii—Ba1—O3vi93.36 (2)O3xv—Mg2—Ba1xx138.48 (2)
O3iv—Ba1—O3vi123.54 (3)O3xvi—Mg2—Ba1xx41.52 (2)
O3v—Ba1—O3vi137.22 (3)O3xvii—Mg2—Ba1xx131.82 (2)
O3i—Ba1—O3vii177.235 (16)O3xviii—Mg2—Ba1xx48.18 (2)
O3ii—Ba1—O3vii57.10 (2)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii43.89 (2)O3xiii—Mg2—Ba1xxi48.18 (2)
O3iv—Ba1—O3vii85.046 (15)O3xiv—Mg2—Ba1xxi131.82 (2)
O3v—Ba1—O3vii84.496 (15)O3xv—Mg2—Ba1xxi98.311 (19)
O3vi—Ba1—O3vii116.57 (2)O3xvi—Mg2—Ba1xxi81.689 (19)
O3i—Ba1—O3viii57.10 (2)O3xvii—Mg2—Ba1xxi41.52 (2)
O3ii—Ba1—O3viii177.235 (16)O3xviii—Mg2—Ba1xxi138.48 (2)
O3iii—Ba1—O3viii85.046 (15)Ba1xix—Mg2—Ba1xxi77.121 (2)
O3iv—Ba1—O3viii43.89 (2)Ba1xx—Mg2—Ba1xxi102.879 (2)
O3v—Ba1—O3viii116.57 (2)O3xiii—Mg2—Ba1xxii131.82 (2)
O3vi—Ba1—O3viii84.496 (15)O3xiv—Mg2—Ba1xxii48.18 (2)
O3vii—Ba1—O3viii122.41 (2)O3xv—Mg2—Ba1xxii81.689 (19)
O3i—Ba1—O3ix43.89 (2)O3xvi—Mg2—Ba1xxii98.311 (19)
O3ii—Ba1—O3ix84.495 (15)O3xvii—Mg2—Ba1xxii138.48 (2)
O3iii—Ba1—O3ix177.235 (17)O3xviii—Mg2—Ba1xxii41.52 (2)
O3iv—Ba1—O3ix116.57 (2)Ba1xix—Mg2—Ba1xxii102.879 (2)
O3v—Ba1—O3ix57.10 (2)Ba1xx—Mg2—Ba1xxii77.121 (2)
O3vi—Ba1—O3ix85.047 (16)Ba1xxi—Mg2—Ba1xxii180.0
O3vii—Ba1—O3ix135.15 (2)O3xiii—Mg2—Ba1xxiii41.52 (2)
O3viii—Ba1—O3ix97.031 (17)O3xiv—Mg2—Ba1xxiii138.48 (2)
O3i—Ba1—O3x84.495 (15)O3xv—Mg2—Ba1xxiii48.18 (2)
O3ii—Ba1—O3x43.89 (2)O3xvi—Mg2—Ba1xxiii131.82 (2)
O3iii—Ba1—O3x116.57 (2)O3xvii—Mg2—Ba1xxiii98.312 (19)
O3iv—Ba1—O3x177.235 (17)O3xviii—Mg2—Ba1xxiii81.688 (19)
O3v—Ba1—O3x85.047 (16)Ba1xix—Mg2—Ba1xxiii77.121 (2)
O3vi—Ba1—O3x57.10 (2)Ba1xx—Mg2—Ba1xxiii102.879 (2)
O3vii—Ba1—O3x97.031 (17)Ba1xxi—Mg2—Ba1xxiii77.121 (2)
O3viii—Ba1—O3x135.15 (2)Ba1xxii—Mg2—Ba1xxiii102.879 (2)
O3ix—Ba1—O3x60.67 (3)O3xiii—Mg2—Ba1iii138.48 (2)
O3i—Ba1—O3xi85.046 (15)O3xiv—Mg2—Ba1iii41.52 (2)
O3ii—Ba1—O3xi116.57 (2)O3xv—Mg2—Ba1iii131.82 (2)
O3iii—Ba1—O3xi57.10 (2)O3xvi—Mg2—Ba1iii48.18 (2)
O3iv—Ba1—O3xi84.496 (15)O3xvii—Mg2—Ba1iii81.688 (19)
O3v—Ba1—O3xi177.235 (16)O3xviii—Mg2—Ba1iii98.312 (19)
O3vi—Ba1—O3xi43.89 (2)Ba1xix—Mg2—Ba1iii102.879 (2)
O3vii—Ba1—O3xi97.031 (17)Ba1xx—Mg2—Ba1iii77.121 (2)
O3viii—Ba1—O3xi60.67 (3)Ba1xxi—Mg2—Ba1iii102.879 (2)
O3ix—Ba1—O3xi122.41 (2)Ba1xxii—Mg2—Ba1iii77.121 (2)
O3x—Ba1—O3xi97.031 (17)Ba1xxiii—Mg2—Ba1iii180.0
O3i—Ba1—O3xii116.57 (2)C4xxiv—O3—Mg2xxv139.37 (6)
O3ii—Ba1—O3xii85.046 (15)C4xxiv—O3—Ba1iii99.64 (4)
O3iii—Ba1—O3xii84.496 (15)Mg2xxv—O3—Ba1iii109.68 (3)
O3iv—Ba1—O3xii57.10 (2)C4xxiv—O3—Ba1x88.94 (4)
O3v—Ba1—O3xii43.89 (2)Mg2xxv—O3—Ba1x101.76 (3)
O3vi—Ba1—O3xii177.235 (16)Ba1iii—O3—Ba1x116.57 (2)
O3vii—Ba1—O3xii60.67 (3)O3xxvi—C4—O3xxvii119.907 (6)
O3viii—Ba1—O3xii97.031 (17)O3xxvi—C4—O3xxviii119.907 (6)
O3ix—Ba1—O3xii97.031 (17)O3xxvii—C4—O3xxviii119.907 (6)
O3x—Ba1—O3xii122.41 (2)O3xxvi—C4—Ba1xxii149.14 (6)
O3xi—Ba1—O3xii135.15 (2)O3xxvii—C4—Ba1xxii68.24 (4)
O3xiii—Mg2—O3xiv180.00 (6)O3xxviii—C4—Ba1xxii57.88 (4)
O3xiii—Mg2—O3xv86.64 (3)O3xxvi—C4—Ba1xx57.88 (4)
O3xiv—Mg2—O3xv93.36 (3)O3xxvii—C4—Ba1xx149.14 (6)
O3xiii—Mg2—O3xvi93.36 (3)O3xxviii—C4—Ba1xx68.24 (4)
O3xiv—Mg2—O3xvi86.64 (3)Ba1xxii—C4—Ba1xx99.053 (18)
O3xv—Mg2—O3xvi180.00 (6)O3xxvi—C4—Ba1iii68.24 (4)
O3xiii—Mg2—O3xvii86.64 (3)O3xxvii—C4—Ba1iii57.88 (4)
O3xiv—Mg2—O3xvii93.36 (3)O3xxviii—C4—Ba1iii149.14 (6)
O3xv—Mg2—O3xvii86.64 (3)Ba1xxii—C4—Ba1iii99.052 (18)
O3xvi—Mg2—O3xvii93.36 (3)Ba1xx—C4—Ba1iii99.052 (18)
O3xiii—Mg2—O3xviii93.36 (3)
Symmetry codes: (i) x+y2/3, y1/3, z+1/6; (ii) y1/3, x+y2/3, z+1/3; (iii) x1/3, y+1/3, z+1/3; (iv) y+1/3, x1/3, z+1/6; (v) x+1/3, xy+2/3, z+1/6; (vi) xy+2/3, x+1/3, z+1/3; (vii) xy+2/3, x2/3, z+1/3; (viii) x2/3, xy+2/3, z+1/6; (ix) y+4/3, x+2/3, z+1/6; (x) x+2/3, y+4/3, z+1/3; (xi) y4/3, x+y2/3, z+1/3; (xii) x+y2/3, y4/3, z+1/6; (xiii) x+y1/3, y2/3, z1/6; (xiv) xy+1/3, y+2/3, z+1/6; (xv) x1/3, xy+1/3, z1/6; (xvi) x+1/3, x+y1/3, z+1/6; (xvii) y+2/3, x+1/3, z1/6; (xviii) y2/3, x1/3, z+1/6; (xix) x2/3, y1/3, z1/3; (xx) x+2/3, y+1/3, z+1/3; (xxi) x+1/3, y+2/3, z1/3; (xxii) x1/3, y2/3, z+1/3; (xxiii) x+1/3, y1/3, z1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, z+1/6; (xxvi) y+1, xy+1, z; (xxvii) x+y1, x, z; (xxviii) x, y1, z.
(norse_320) top
Crystal data top
C6Ba3Mg3O18Dx = 3.841 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 9499 reflections
a = 5.0180 (1) Åθ = 1.5–45°
c = 33.5012 (8) ŵ = 8.24 mm1
V = 730.55 (3) Å3T = 320 K
Z = 2Prismatic
F(000) = 7680.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.030
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.6°, θmin = 3.7°
Tmin = 0.7, Tmax = 0.8h = 109
9499 measured reflectionsk = 910
701 independent reflectionsl = 3666
484 reflections with I > 2σ(I)
Refinement top
Refinement on F217 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.010 w = 1/[σ2(Fo2) + (0.0134P)2]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.023(Δ/σ)max < 0.001
S = 0.97Δρmax = 0.51 e Å3
701 reflectionsΔρmin = 0.42 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.25000.01119 (2)
Mg20.00000.00000.00000.00893 (7)
O30.1219 (2)0.82952 (19)0.12915 (2)0.02110 (14)
C40.00000.00000.13038 (3)0.00949 (11)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.00978 (2)0.00978 (2)0.01400 (3)0.00489 (1)0.0000.000
Mg20.00767 (11)0.00767 (11)0.01146 (17)0.00383 (5)0.0000.000
O30.0284 (4)0.0241 (4)0.0227 (2)0.0221 (3)0.0088 (3)0.0053 (3)
C40.00917 (17)0.00917 (17)0.0101 (3)0.00459 (9)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.8435 (8)Mg2—O3xviii2.0591 (6)
Ba1—O3ii2.8435 (8)Mg2—Ba1xix4.0234 (1)
Ba1—O3iii2.8435 (9)Mg2—Ba1xx4.0234 (1)
Ba1—O3iv2.8435 (9)Mg2—Ba1xxi4.0234 (1)
Ba1—O3v2.8435 (8)Mg2—Ba1xxii4.0234 (1)
Ba1—O3vi2.8435 (8)Mg2—Ba1iii4.0234 (1)
Ba1—O3vii3.0511 (9)Mg2—Ba1xxiii4.0234 (1)
Ba1—O3viii3.0511 (9)O3—C4xxiv1.2771 (6)
Ba1—O3ix3.0511 (9)O3—Mg2xxv2.0592 (6)
Ba1—O3x3.0511 (9)O3—Ba1iii2.8435 (8)
Ba1—O3xi3.0511 (9)O3—Ba1x3.0511 (9)
Ba1—O3xii3.0511 (9)C4—O3xxvi1.2771 (6)
Mg2—O3xiii2.0591 (6)C4—O3xxvii1.2771 (6)
Mg2—O3xiv2.0591 (6)C4—O3xxviii1.2771 (6)
Mg2—O3xv2.0591 (6)C4—Ba1xxii3.2980 (4)
Mg2—O3xvi2.0591 (6)C4—Ba1xx3.2980 (4)
Mg2—O3xvii2.0591 (6)C4—Ba1iii3.2981 (4)
O3i—Ba1—O3ii123.42 (3)O3xiv—Mg2—O3xviii86.63 (3)
O3i—Ba1—O3iii137.12 (3)O3xv—Mg2—O3xviii93.37 (3)
O3ii—Ba1—O3iii93.61 (2)O3xvi—Mg2—O3xviii86.63 (3)
O3i—Ba1—O3iv93.61 (2)O3xvii—Mg2—O3xviii180.00 (5)
O3ii—Ba1—O3iv137.12 (3)O3xiii—Mg2—Ba1xix41.85 (2)
O3iii—Ba1—O3iv65.83 (3)O3xiv—Mg2—Ba1xix138.15 (2)
O3i—Ba1—O3v93.61 (2)O3xv—Mg2—Ba1xix98.35 (2)
O3ii—Ba1—O3v65.83 (3)O3xvi—Mg2—Ba1xix81.65 (2)
O3iii—Ba1—O3v123.42 (3)O3xvii—Mg2—Ba1xix47.86 (3)
O3iv—Ba1—O3v93.61 (2)O3xviii—Mg2—Ba1xix132.14 (3)
O3i—Ba1—O3vi65.83 (3)O3xiii—Mg2—Ba1xx138.15 (2)
O3ii—Ba1—O3vi93.61 (2)O3xiv—Mg2—Ba1xx41.85 (2)
O3iii—Ba1—O3vi93.61 (2)O3xv—Mg2—Ba1xx81.65 (2)
O3iv—Ba1—O3vi123.42 (3)O3xvi—Mg2—Ba1xx98.35 (2)
O3v—Ba1—O3vi137.12 (3)O3xvii—Mg2—Ba1xx132.14 (3)
O3i—Ba1—O3vii177.511 (19)O3xviii—Mg2—Ba1xx47.86 (3)
O3ii—Ba1—O3vii57.15 (2)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii43.88 (2)O3xiii—Mg2—Ba1xxi98.35 (2)
O3iv—Ba1—O3vii84.957 (16)O3xiv—Mg2—Ba1xxi81.65 (2)
O3v—Ba1—O3vii84.459 (16)O3xv—Mg2—Ba1xxi47.86 (2)
O3vi—Ba1—O3vii116.66 (2)O3xvi—Mg2—Ba1xxi132.14 (2)
O3i—Ba1—O3viii57.15 (2)O3xvii—Mg2—Ba1xxi41.86 (2)
O3ii—Ba1—O3viii177.511 (19)O3xviii—Mg2—Ba1xxi138.14 (2)
O3iii—Ba1—O3viii84.957 (16)Ba1xix—Mg2—Ba1xxi77.159 (1)
O3iv—Ba1—O3viii43.88 (2)Ba1xx—Mg2—Ba1xxi102.841 (1)
O3v—Ba1—O3viii116.66 (2)O3xiii—Mg2—Ba1xxii81.65 (2)
O3vi—Ba1—O3viii84.459 (16)O3xiv—Mg2—Ba1xxii98.35 (2)
O3vii—Ba1—O3viii122.41 (2)O3xv—Mg2—Ba1xxii132.14 (2)
O3i—Ba1—O3ix43.88 (3)O3xvi—Mg2—Ba1xxii47.86 (2)
O3ii—Ba1—O3ix84.458 (16)O3xvii—Mg2—Ba1xxii138.14 (2)
O3iii—Ba1—O3ix177.51 (2)O3xviii—Mg2—Ba1xxii41.86 (2)
O3iv—Ba1—O3ix116.66 (2)Ba1xix—Mg2—Ba1xxii102.841 (1)
O3v—Ba1—O3ix57.15 (2)Ba1xx—Mg2—Ba1xxii77.159 (1)
O3vi—Ba1—O3ix84.958 (16)Ba1xxi—Mg2—Ba1xxii180.0
O3vii—Ba1—O3ix135.26 (2)O3xiii—Mg2—Ba1iii132.14 (2)
O3viii—Ba1—O3ix96.917 (18)O3xiv—Mg2—Ba1iii47.86 (2)
O3i—Ba1—O3x84.458 (16)O3xv—Mg2—Ba1iii138.14 (2)
O3ii—Ba1—O3x43.88 (3)O3xvi—Mg2—Ba1iii41.86 (2)
O3iii—Ba1—O3x116.66 (2)O3xvii—Mg2—Ba1iii81.64 (2)
O3iv—Ba1—O3x177.51 (2)O3xviii—Mg2—Ba1iii98.36 (2)
O3v—Ba1—O3x84.958 (16)Ba1xix—Mg2—Ba1iii102.841 (1)
O3vi—Ba1—O3x57.15 (2)Ba1xx—Mg2—Ba1iii77.159 (1)
O3vii—Ba1—O3x96.917 (18)Ba1xxi—Mg2—Ba1iii102.841 (1)
O3viii—Ba1—O3x135.26 (2)Ba1xxii—Mg2—Ba1iii77.159 (1)
O3ix—Ba1—O3x60.85 (3)O3xiii—Mg2—Ba1xxiii47.86 (2)
O3i—Ba1—O3xi84.957 (16)O3xiv—Mg2—Ba1xxiii132.14 (2)
O3ii—Ba1—O3xi116.66 (2)O3xv—Mg2—Ba1xxiii41.86 (2)
O3iii—Ba1—O3xi57.15 (2)O3xvi—Mg2—Ba1xxiii138.14 (2)
O3iv—Ba1—O3xi84.459 (16)O3xvii—Mg2—Ba1xxiii98.36 (2)
O3v—Ba1—O3xi177.511 (19)O3xviii—Mg2—Ba1xxiii81.64 (2)
O3vi—Ba1—O3xi43.88 (3)Ba1xix—Mg2—Ba1xxiii77.159 (1)
O3vii—Ba1—O3xi96.916 (18)Ba1xx—Mg2—Ba1xxiii102.841 (1)
O3viii—Ba1—O3xi60.85 (3)Ba1xxi—Mg2—Ba1xxiii77.159 (1)
O3ix—Ba1—O3xi122.41 (2)Ba1xxii—Mg2—Ba1xxiii102.841 (1)
O3x—Ba1—O3xi96.916 (18)Ba1iii—Mg2—Ba1xxiii180.0
O3i—Ba1—O3xii116.66 (2)C4xxiv—O3—Mg2xxv139.51 (6)
O3ii—Ba1—O3xii84.957 (16)C4xxiv—O3—Ba1iii99.20 (5)
O3iii—Ba1—O3xii84.459 (16)Mg2xxv—O3—Ba1iii109.25 (3)
O3iv—Ba1—O3xii57.15 (2)C4xxiv—O3—Ba1x89.54 (5)
O3v—Ba1—O3xii43.88 (3)Mg2xxv—O3—Ba1x102.12 (3)
O3vi—Ba1—O3xii177.511 (19)Ba1iii—O3—Ba1x116.66 (2)
O3vii—Ba1—O3xii60.85 (3)O3xxvi—C4—O3xxvii119.897 (6)
O3viii—Ba1—O3xii96.916 (18)O3xxvi—C4—O3xxviii119.897 (6)
O3ix—Ba1—O3xii96.916 (18)O3xxvii—C4—O3xxviii119.897 (6)
O3x—Ba1—O3xii122.41 (2)O3xxvi—C4—Ba1xxii149.16 (6)
O3xi—Ba1—O3xii135.26 (3)O3xxvii—C4—Ba1xxii67.68 (4)
O3xiii—Mg2—O3xiv180.00 (6)O3xxviii—C4—Ba1xxii58.33 (4)
O3xiii—Mg2—O3xv86.63 (3)O3xxvi—C4—Ba1xx58.33 (4)
O3xiv—Mg2—O3xv93.37 (3)O3xxvii—C4—Ba1xx149.16 (6)
O3xiii—Mg2—O3xvi93.37 (3)O3xxviii—C4—Ba1xx67.68 (4)
O3xiv—Mg2—O3xvi86.63 (3)Ba1xxii—C4—Ba1xx99.062 (17)
O3xv—Mg2—O3xvi180.00 (7)O3xxvi—C4—Ba1iii67.68 (4)
O3xiii—Mg2—O3xvii86.63 (3)O3xxvii—C4—Ba1iii58.33 (4)
O3xiv—Mg2—O3xvii93.37 (3)O3xxviii—C4—Ba1iii149.16 (6)
O3xv—Mg2—O3xvii86.63 (3)Ba1xxii—C4—Ba1iii99.062 (17)
O3xvi—Mg2—O3xvii93.37 (3)Ba1xx—C4—Ba1iii99.062 (17)
O3xiii—Mg2—O3xviii93.37 (3)
Symmetry codes: (i) x+y2/3, y1/3, z+1/6; (ii) y1/3, x+y2/3, z+1/3; (iii) x1/3, y+1/3, z+1/3; (iv) y+1/3, x1/3, z+1/6; (v) x+1/3, xy+2/3, z+1/6; (vi) xy+2/3, x+1/3, z+1/3; (vii) xy+2/3, x2/3, z+1/3; (viii) x2/3, xy+2/3, z+1/6; (ix) y+4/3, x+2/3, z+1/6; (x) x+2/3, y+4/3, z+1/3; (xi) y4/3, x+y2/3, z+1/3; (xii) x+y2/3, y4/3, z+1/6; (xiii) x1/3, xy+1/3, z1/6; (xiv) x+1/3, x+y1/3, z+1/6; (xv) x+y1/3, y2/3, z1/6; (xvi) xy+1/3, y+2/3, z+1/6; (xvii) y+2/3, x+1/3, z1/6; (xviii) y2/3, x1/3, z+1/6; (xix) x2/3, y1/3, z1/3; (xx) x+2/3, y+1/3, z+1/3; (xxi) x+1/3, y+2/3, z1/3; (xxii) x1/3, y2/3, z+1/3; (xxiii) x+1/3, y1/3, z1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, z+1/6; (xxvi) y+1, xy+1, z; (xxvii) x+y1, x, z; (xxviii) x, y1, z.
(norse_330) top
Crystal data top
C6Ba3Mg3O18Dx = 3.840 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 9461 reflections
a = 5.0183 (1) Åθ = 1.5–45°
c = 33.5074 (8) ŵ = 8.24 mm1
V = 730.78 (3) Å3T = 330 K
Z = 2Prismatic
F(000) = 7680.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.029
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.6°, θmin = 3.7°
Tmin = 0.7, Tmax = 0.8h = 109
9461 measured reflectionsk = 910
701 independent reflectionsl = 3466
477 reflections with I > 2σ(I)
Refinement top
Refinement on F217 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.011 w = 1/[σ2(Fo2) + (0.0138P)2]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.024(Δ/σ)max < 0.001
S = 1.01Δρmax = 0.57 e Å3
701 reflectionsΔρmin = 0.41 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.25000.01163 (2)
Mg20.00000.00000.00000.00926 (8)
O30.1239 (2)0.8315 (2)0.12914 (2)0.02222 (15)
C40.00000.00000.13038 (3)0.00966 (12)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.01018 (3)0.01018 (3)0.01453 (4)0.00509 (1)0.0000.000
Mg20.00787 (11)0.00787 (11)0.01206 (18)0.00393 (6)0.0000.000
O30.0302 (4)0.0257 (4)0.0235 (2)0.0236 (4)0.0094 (3)0.0057 (3)
C40.00945 (18)0.00945 (18)0.0101 (3)0.00473 (9)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.8518 (9)Mg2—O3xviii2.0589 (7)
Ba1—O3ii2.8518 (9)Mg2—Ba1xix4.0239 (1)
Ba1—O3iii2.8518 (10)Mg2—Ba1xx4.0239 (1)
Ba1—O3iv2.8518 (10)Mg2—Ba1xxi4.0239 (1)
Ba1—O3v2.8518 (9)Mg2—Ba1xxii4.0239 (1)
Ba1—O3vi2.8518 (9)Mg2—Ba1iii4.0238 (1)
Ba1—O3vii3.0426 (10)Mg2—Ba1xxiii4.0238 (1)
Ba1—O3viii3.0426 (10)O3—C4xxiv1.2766 (7)
Ba1—O3ix3.0426 (10)O3—Mg2xxv2.0589 (7)
Ba1—O3x3.0426 (10)O3—Ba1iii2.8518 (9)
Ba1—O3xi3.0426 (10)O3—Ba1x3.0426 (10)
Ba1—O3xii3.0426 (10)C4—O3xxvi1.2766 (7)
Mg2—O3xiii2.0589 (7)C4—O3xxvii1.2766 (7)
Mg2—O3xiv2.0589 (7)C4—O3xxviii1.2766 (7)
Mg2—O3xv2.0589 (7)C4—Ba1xxii3.2984 (4)
Mg2—O3xvi2.0589 (7)C4—Ba1xx3.2984 (5)
Mg2—O3xvii2.0589 (7)C4—Ba1iii3.2984 (4)
O3i—Ba1—O3ii123.38 (3)O3xiv—Mg2—O3xviii86.58 (3)
O3i—Ba1—O3iii137.02 (3)O3xv—Mg2—O3xviii93.42 (3)
O3ii—Ba1—O3iii93.76 (2)O3xvi—Mg2—O3xviii86.58 (3)
O3i—Ba1—O3iv93.76 (2)O3xvii—Mg2—O3xviii180.00 (5)
O3ii—Ba1—O3iv137.02 (3)O3xiii—Mg2—Ba1xix42.08 (3)
O3iii—Ba1—O3iv65.60 (4)O3xiv—Mg2—Ba1xix137.92 (3)
O3i—Ba1—O3v93.76 (2)O3xv—Mg2—Ba1xix98.33 (2)
O3ii—Ba1—O3v65.60 (3)O3xvi—Mg2—Ba1xix81.67 (2)
O3iii—Ba1—O3v123.38 (3)O3xvii—Mg2—Ba1xix47.60 (3)
O3iv—Ba1—O3v93.76 (2)O3xviii—Mg2—Ba1xix132.40 (3)
O3i—Ba1—O3vi65.60 (3)O3xiii—Mg2—Ba1xx137.92 (3)
O3ii—Ba1—O3vi93.76 (2)O3xiv—Mg2—Ba1xx42.08 (3)
O3iii—Ba1—O3vi93.76 (2)O3xv—Mg2—Ba1xx81.67 (2)
O3iv—Ba1—O3vi123.38 (3)O3xvi—Mg2—Ba1xx98.33 (2)
O3v—Ba1—O3vi137.02 (3)O3xvii—Mg2—Ba1xx132.40 (3)
O3i—Ba1—O3vii177.71 (2)O3xviii—Mg2—Ba1xx47.60 (3)
O3ii—Ba1—O3vii57.14 (3)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii43.89 (3)O3xiii—Mg2—Ba1xxi98.33 (2)
O3iv—Ba1—O3vii84.922 (17)O3xiv—Mg2—Ba1xxi81.67 (2)
O3v—Ba1—O3vii84.465 (16)O3xv—Mg2—Ba1xxi47.60 (3)
O3vi—Ba1—O3vii116.69 (2)O3xvi—Mg2—Ba1xxi132.40 (3)
O3i—Ba1—O3viii57.14 (3)O3xvii—Mg2—Ba1xxi42.08 (3)
O3ii—Ba1—O3viii177.71 (2)O3xviii—Mg2—Ba1xxi137.92 (3)
O3iii—Ba1—O3viii84.922 (17)Ba1xix—Mg2—Ba1xxi77.154 (1)
O3iv—Ba1—O3viii43.89 (3)Ba1xx—Mg2—Ba1xxi102.846 (1)
O3v—Ba1—O3viii116.69 (2)O3xiii—Mg2—Ba1xxii81.67 (2)
O3vi—Ba1—O3viii84.465 (16)O3xiv—Mg2—Ba1xxii98.33 (2)
O3vii—Ba1—O3viii122.45 (3)O3xv—Mg2—Ba1xxii132.40 (3)
O3i—Ba1—O3ix43.89 (3)O3xvi—Mg2—Ba1xxii47.60 (3)
O3ii—Ba1—O3ix84.465 (16)O3xvii—Mg2—Ba1xxii137.92 (3)
O3iii—Ba1—O3ix177.71 (2)O3xviii—Mg2—Ba1xxii42.08 (3)
O3iv—Ba1—O3ix116.69 (2)Ba1xix—Mg2—Ba1xxii102.846 (1)
O3v—Ba1—O3ix57.13 (3)Ba1xx—Mg2—Ba1xxii77.154 (1)
O3vi—Ba1—O3ix84.923 (17)Ba1xxi—Mg2—Ba1xxii180.0
O3vii—Ba1—O3ix135.31 (3)O3xiii—Mg2—Ba1iii132.40 (3)
O3viii—Ba1—O3ix96.80 (2)O3xiv—Mg2—Ba1iii47.60 (3)
O3i—Ba1—O3x84.465 (16)O3xv—Mg2—Ba1iii137.92 (3)
O3ii—Ba1—O3x43.89 (3)O3xvi—Mg2—Ba1iii42.08 (3)
O3iii—Ba1—O3x116.69 (2)O3xvii—Mg2—Ba1iii81.67 (2)
O3iv—Ba1—O3x177.71 (2)O3xviii—Mg2—Ba1iii98.33 (2)
O3v—Ba1—O3x84.923 (17)Ba1xix—Mg2—Ba1iii102.847 (2)
O3vi—Ba1—O3x57.13 (3)Ba1xx—Mg2—Ba1iii77.153 (1)
O3vii—Ba1—O3x96.80 (2)Ba1xxi—Mg2—Ba1iii102.847 (1)
O3viii—Ba1—O3x135.31 (3)Ba1xxii—Mg2—Ba1iii77.153 (1)
O3ix—Ba1—O3x61.03 (3)O3xiii—Mg2—Ba1xxiii47.60 (3)
O3i—Ba1—O3xi84.923 (17)O3xiv—Mg2—Ba1xxiii132.40 (3)
O3ii—Ba1—O3xi116.69 (2)O3xv—Mg2—Ba1xxiii42.08 (3)
O3iii—Ba1—O3xi57.13 (3)O3xvi—Mg2—Ba1xxiii137.92 (3)
O3iv—Ba1—O3xi84.465 (16)O3xvii—Mg2—Ba1xxiii98.33 (2)
O3v—Ba1—O3xi177.71 (2)O3xviii—Mg2—Ba1xxiii81.67 (2)
O3vi—Ba1—O3xi43.89 (3)Ba1xix—Mg2—Ba1xxiii77.153 (1)
O3vii—Ba1—O3xi96.80 (2)Ba1xx—Mg2—Ba1xxiii102.847 (2)
O3viii—Ba1—O3xi61.03 (3)Ba1xxi—Mg2—Ba1xxiii77.153 (1)
O3ix—Ba1—O3xi122.45 (3)Ba1xxii—Mg2—Ba1xxiii102.847 (1)
O3x—Ba1—O3xi96.80 (2)Ba1iii—Mg2—Ba1xxiii180.0
O3i—Ba1—O3xii116.69 (2)C4xxiv—O3—Mg2xxv139.62 (7)
O3ii—Ba1—O3xii84.923 (17)C4xxiv—O3—Ba1iii98.82 (5)
O3iii—Ba1—O3xii84.465 (16)Mg2xxv—O3—Ba1iii108.98 (3)
O3iv—Ba1—O3xii57.13 (3)C4xxiv—O3—Ba1x89.94 (5)
O3v—Ba1—O3xii43.89 (3)Mg2xxv—O3—Ba1x102.42 (3)
O3vi—Ba1—O3xii177.71 (2)Ba1iii—O3—Ba1x116.68 (2)
O3vii—Ba1—O3xii61.03 (3)O3xxvi—C4—O3xxvii119.894 (7)
O3viii—Ba1—O3xii96.80 (2)O3xxvi—C4—O3xxviii119.894 (7)
O3ix—Ba1—O3xii96.80 (2)O3xxvii—C4—O3xxviii119.894 (6)
O3x—Ba1—O3xii122.45 (3)O3xxvi—C4—Ba1xxii149.19 (6)
O3xi—Ba1—O3xii135.31 (3)O3xxvii—C4—Ba1xxii67.29 (5)
O3xiii—Mg2—O3xiv180.00 (4)O3xxviii—C4—Ba1xxii58.69 (5)
O3xiii—Mg2—O3xv86.59 (3)O3xxvi—C4—Ba1xx58.69 (5)
O3xiv—Mg2—O3xv93.41 (3)O3xxvii—C4—Ba1xx149.19 (6)
O3xiii—Mg2—O3xvi93.41 (3)O3xxviii—C4—Ba1xx67.29 (5)
O3xiv—Mg2—O3xvi86.59 (3)Ba1xxii—C4—Ba1xx99.056 (18)
O3xv—Mg2—O3xvi180.00 (7)O3xxvi—C4—Ba1iii67.29 (5)
O3xiii—Mg2—O3xvii86.58 (3)O3xxvii—C4—Ba1iii58.69 (5)
O3xiv—Mg2—O3xvii93.42 (3)O3xxviii—C4—Ba1iii149.20 (6)
O3xv—Mg2—O3xvii86.58 (3)Ba1xxii—C4—Ba1iii99.055 (18)
O3xvi—Mg2—O3xvii93.42 (3)Ba1xx—C4—Ba1iii99.055 (18)
O3xiii—Mg2—O3xviii93.42 (3)
Symmetry codes: (i) x+y2/3, y1/3, z+1/6; (ii) y1/3, x+y2/3, z+1/3; (iii) x1/3, y+1/3, z+1/3; (iv) y+1/3, x1/3, z+1/6; (v) x+1/3, xy+2/3, z+1/6; (vi) xy+2/3, x+1/3, z+1/3; (vii) xy+2/3, x2/3, z+1/3; (viii) x2/3, xy+2/3, z+1/6; (ix) y+4/3, x+2/3, z+1/6; (x) x+2/3, y+4/3, z+1/3; (xi) y4/3, x+y2/3, z+1/3; (xii) x+y2/3, y4/3, z+1/6; (xiii) x1/3, xy+1/3, z1/6; (xiv) x+1/3, x+y1/3, z+1/6; (xv) x+y1/3, y2/3, z1/6; (xvi) xy+1/3, y+2/3, z+1/6; (xvii) y+2/3, x+1/3, z1/6; (xviii) y2/3, x1/3, z+1/6; (xix) x2/3, y1/3, z1/3; (xx) x+2/3, y+1/3, z+1/3; (xxi) x+1/3, y+2/3, z1/3; (xxii) x1/3, y2/3, z+1/3; (xxiii) x+1/3, y1/3, z1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, z+1/6; (xxvi) y+1, xy+1, z; (xxvii) x+y1, x, z; (xxviii) x, y1, z.
(norse_340) top
Crystal data top
C6Ba3Mg3O18Dx = 3.837 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 9472 reflections
a = 5.0187 (1) Åθ = 1.5–45°
c = 33.5273 (9) ŵ = 8.23 mm1
V = 731.33 (4) Å3T = 340 K
Z = 2Prismatic
F(000) = 7680.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.029
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.6°, θmin = 3.7°
Tmin = 0.7, Tmax = 0.8h = 109
9472 measured reflectionsk = 910
700 independent reflectionsl = 3466
474 reflections with I > 2σ(I)
Refinement top
Refinement on F217 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.011 w = 1/[σ2(Fo2) + (0.0119P)2 + 0.6958P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.025(Δ/σ)max < 0.001
S = 0.98Δρmax = 0.77 e Å3
700 reflectionsΔρmin = 0.55 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.25000.01198 (2)
Mg20.00000.00000.00000.00956 (8)
O30.1256 (3)0.8333 (3)0.12912 (2)0.02315 (17)
C40.00000.00000.13035 (3)0.00997 (13)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.01049 (3)0.01049 (3)0.01495 (4)0.00524 (1)0.0000.000
Mg20.00826 (12)0.00826 (12)0.0122 (2)0.00413 (6)0.0000.000
O30.0325 (5)0.0262 (4)0.0244 (3)0.0249 (4)0.0103 (4)0.0062 (4)
C40.00959 (19)0.00959 (19)0.0107 (3)0.00479 (10)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.8598 (11)Mg2—O3xviii2.0594 (7)
Ba1—O3ii2.8598 (11)Mg2—Ba1xix4.0252 (1)
Ba1—O3iii2.8598 (11)Mg2—Ba1xx4.0252 (1)
Ba1—O3iv2.8598 (11)Mg2—Ba1xxi4.0252 (1)
Ba1—O3v2.8598 (11)Mg2—Ba1xxii4.0252 (1)
Ba1—O3vi2.8598 (11)Mg2—Ba1iii4.0252 (1)
Ba1—O3vii3.0355 (12)Mg2—Ba1xxiii4.0252 (1)
Ba1—O3viii3.0355 (12)O3—C4xxiv1.2755 (7)
Ba1—O3ix3.0355 (12)O3—Mg2xxv2.0595 (7)
Ba1—O3x3.0355 (12)O3—Ba1iii2.8597 (11)
Ba1—O3xi3.0355 (12)O3—Ba1x3.0354 (12)
Ba1—O3xii3.0355 (12)C4—O3xxvi1.2755 (7)
Mg2—O3xiii2.0594 (7)C4—O3xxvii1.2755 (7)
Mg2—O3xiv2.0594 (7)C4—O3xxviii1.2755 (7)
Mg2—O3xv2.0594 (7)C4—Ba1xxii3.2985 (5)
Mg2—O3xvi2.0594 (7)C4—Ba1xx3.2985 (5)
Mg2—O3xvii2.0594 (7)C4—Ba1iii3.2985 (5)
O3i—Ba1—O3ii123.33 (3)O3xiv—Mg2—O3xviii86.55 (3)
O3i—Ba1—O3iii136.97 (3)O3xv—Mg2—O3xviii93.45 (3)
O3ii—Ba1—O3iii93.88 (3)O3xvi—Mg2—O3xviii86.55 (3)
O3i—Ba1—O3iv93.88 (3)O3xvii—Mg2—O3xviii180.00 (6)
O3ii—Ba1—O3iv136.97 (3)O3xiii—Mg2—Ba1xix42.29 (3)
O3iii—Ba1—O3iv65.43 (4)O3xiv—Mg2—Ba1xix137.71 (3)
O3i—Ba1—O3v93.88 (3)O3xv—Mg2—Ba1xix98.31 (2)
O3ii—Ba1—O3v65.43 (4)O3xvi—Mg2—Ba1xix81.69 (2)
O3iii—Ba1—O3v123.33 (3)O3xvii—Mg2—Ba1xix47.37 (3)
O3iv—Ba1—O3v93.88 (3)O3xviii—Mg2—Ba1xix132.63 (3)
O3i—Ba1—O3vi65.43 (4)O3xiii—Mg2—Ba1xx137.71 (3)
O3ii—Ba1—O3vi93.88 (3)O3xiv—Mg2—Ba1xx42.29 (3)
O3iii—Ba1—O3vi93.88 (3)O3xv—Mg2—Ba1xx81.69 (2)
O3iv—Ba1—O3vi123.33 (3)O3xvi—Mg2—Ba1xx98.31 (2)
O3v—Ba1—O3vi136.97 (3)O3xvii—Mg2—Ba1xx132.63 (3)
O3i—Ba1—O3vii177.89 (3)O3xviii—Mg2—Ba1xx47.37 (3)
O3ii—Ba1—O3vii57.14 (3)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii43.87 (3)O3xiii—Mg2—Ba1xxi98.31 (2)
O3iv—Ba1—O3vii84.910 (18)O3xiv—Mg2—Ba1xxi81.69 (2)
O3v—Ba1—O3vii84.489 (17)O3xv—Mg2—Ba1xxi47.37 (3)
O3vi—Ba1—O3vii116.68 (3)O3xvi—Mg2—Ba1xxi132.63 (3)
O3i—Ba1—O3viii57.14 (3)O3xvii—Mg2—Ba1xxi42.29 (3)
O3ii—Ba1—O3viii177.89 (3)O3xviii—Mg2—Ba1xxi137.71 (3)
O3iii—Ba1—O3viii84.910 (18)Ba1xix—Mg2—Ba1xxi77.131 (2)
O3iv—Ba1—O3viii43.87 (3)Ba1xx—Mg2—Ba1xxi102.869 (2)
O3v—Ba1—O3viii116.68 (3)O3xiii—Mg2—Ba1xxii81.69 (2)
O3vi—Ba1—O3viii84.489 (17)O3xiv—Mg2—Ba1xxii98.31 (2)
O3vii—Ba1—O3viii122.48 (3)O3xv—Mg2—Ba1xxii132.63 (3)
O3i—Ba1—O3ix43.87 (3)O3xvi—Mg2—Ba1xxii47.37 (3)
O3ii—Ba1—O3ix84.488 (17)O3xvii—Mg2—Ba1xxii137.71 (3)
O3iii—Ba1—O3ix177.89 (3)O3xviii—Mg2—Ba1xxii42.29 (3)
O3iv—Ba1—O3ix116.68 (3)Ba1xix—Mg2—Ba1xxii102.869 (2)
O3v—Ba1—O3ix57.14 (3)Ba1xx—Mg2—Ba1xxii77.131 (2)
O3vi—Ba1—O3ix84.911 (18)Ba1xxi—Mg2—Ba1xxii180.0
O3vii—Ba1—O3ix135.39 (3)O3xiii—Mg2—Ba1iii132.63 (3)
O3viii—Ba1—O3ix96.68 (2)O3xiv—Mg2—Ba1iii47.37 (3)
O3i—Ba1—O3x84.488 (17)O3xv—Mg2—Ba1iii137.71 (3)
O3ii—Ba1—O3x43.87 (3)O3xvi—Mg2—Ba1iii42.29 (3)
O3iii—Ba1—O3x116.68 (3)O3xvii—Mg2—Ba1iii81.69 (2)
O3iv—Ba1—O3x177.89 (3)O3xviii—Mg2—Ba1iii98.31 (2)
O3v—Ba1—O3x84.911 (18)Ba1xix—Mg2—Ba1iii102.869 (1)
O3vi—Ba1—O3x57.14 (3)Ba1xx—Mg2—Ba1iii77.131 (1)
O3vii—Ba1—O3x96.68 (2)Ba1xxi—Mg2—Ba1iii102.869 (2)
O3viii—Ba1—O3x135.39 (3)Ba1xxii—Mg2—Ba1iii77.131 (2)
O3ix—Ba1—O3x61.22 (3)O3xiii—Mg2—Ba1xxiii47.37 (3)
O3i—Ba1—O3xi84.911 (18)O3xiv—Mg2—Ba1xxiii132.63 (3)
O3ii—Ba1—O3xi116.68 (3)O3xv—Mg2—Ba1xxiii42.29 (3)
O3iii—Ba1—O3xi57.14 (3)O3xvi—Mg2—Ba1xxiii137.71 (3)
O3iv—Ba1—O3xi84.489 (17)O3xvii—Mg2—Ba1xxiii98.31 (2)
O3v—Ba1—O3xi177.89 (3)O3xviii—Mg2—Ba1xxiii81.69 (2)
O3vi—Ba1—O3xi43.87 (3)Ba1xix—Mg2—Ba1xxiii77.131 (1)
O3vii—Ba1—O3xi96.68 (2)Ba1xx—Mg2—Ba1xxiii102.869 (1)
O3viii—Ba1—O3xi61.22 (3)Ba1xxi—Mg2—Ba1xxiii77.131 (2)
O3ix—Ba1—O3xi122.48 (3)Ba1xxii—Mg2—Ba1xxiii102.869 (2)
O3x—Ba1—O3xi96.68 (2)Ba1iii—Mg2—Ba1xxiii180.0
O3i—Ba1—O3xii116.68 (3)C4xxiv—O3—Mg2xxv139.75 (7)
O3ii—Ba1—O3xii84.911 (18)C4xxiv—O3—Ba1iii98.47 (6)
O3iii—Ba1—O3xii84.489 (17)Mg2xxv—O3—Ba1iii108.73 (4)
O3iv—Ba1—O3xii57.14 (3)C4xxiv—O3—Ba1x90.29 (6)
O3v—Ba1—O3xii43.87 (3)Mg2xxv—O3—Ba1x102.69 (4)
O3vi—Ba1—O3xii177.89 (3)Ba1iii—O3—Ba1x116.68 (3)
O3vii—Ba1—O3xii61.22 (3)O3xxvi—C4—O3xxvii119.898 (7)
O3viii—Ba1—O3xii96.68 (2)O3xxvi—C4—O3xxviii119.898 (7)
O3ix—Ba1—O3xii96.68 (2)O3xxvii—C4—O3xxviii119.898 (7)
O3x—Ba1—O3xii122.48 (3)O3xxvi—C4—Ba1xxii149.29 (7)
O3xi—Ba1—O3xii135.39 (3)O3xxvii—C4—Ba1xxii66.96 (6)
O3xiii—Mg2—O3xiv180.00 (8)O3xxviii—C4—Ba1xxii59.04 (5)
O3xiii—Mg2—O3xv86.55 (3)O3xxvi—C4—Ba1xx59.04 (5)
O3xiv—Mg2—O3xv93.45 (3)O3xxvii—C4—Ba1xx149.29 (7)
O3xiii—Mg2—O3xvi93.45 (3)O3xxviii—C4—Ba1xx66.96 (6)
O3xiv—Mg2—O3xvi86.55 (3)Ba1xxii—C4—Ba1xx99.06 (2)
O3xv—Mg2—O3xvi180.00 (9)O3xxvi—C4—Ba1iii66.96 (6)
O3xiii—Mg2—O3xvii86.55 (3)O3xxvii—C4—Ba1iii59.04 (5)
O3xiv—Mg2—O3xvii93.45 (3)O3xxviii—C4—Ba1iii149.29 (7)
O3xv—Mg2—O3xvii86.55 (3)Ba1xxii—C4—Ba1iii99.06 (2)
O3xvi—Mg2—O3xvii93.45 (3)Ba1xx—C4—Ba1iii99.06 (2)
O3xiii—Mg2—O3xviii93.45 (3)
Symmetry codes: (i) x+y2/3, y1/3, z+1/6; (ii) y1/3, x+y2/3, z+1/3; (iii) x1/3, y+1/3, z+1/3; (iv) y+1/3, x1/3, z+1/6; (v) x+1/3, xy+2/3, z+1/6; (vi) xy+2/3, x+1/3, z+1/3; (vii) xy+2/3, x2/3, z+1/3; (viii) x2/3, xy+2/3, z+1/6; (ix) y+4/3, x+2/3, z+1/6; (x) x+2/3, y+4/3, z+1/3; (xi) y4/3, x+y2/3, z+1/3; (xii) x+y2/3, y4/3, z+1/6; (xiii) x1/3, xy+1/3, z1/6; (xiv) x+1/3, x+y1/3, z+1/6; (xv) x+y1/3, y2/3, z1/6; (xvi) xy+1/3, y+2/3, z+1/6; (xvii) y+2/3, x+1/3, z1/6; (xviii) y2/3, x1/3, z+1/6; (xix) x2/3, y1/3, z1/3; (xx) x+2/3, y+1/3, z+1/3; (xxi) x+1/3, y+2/3, z1/3; (xxii) x1/3, y2/3, z+1/3; (xxiii) x+1/3, y1/3, z1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, z+1/6; (xxvi) y+1, xy+1, z; (xxvii) x+y1, x, z; (xxviii) x, y1, z.
(norse_350) top
Crystal data top
C6Ba3Mg3O18Dx = 3.837 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 9486 reflections
a = 5.0198 (1) Åθ = 1.5–45°
c = 33.5169 (9) ŵ = 8.23 mm1
V = 731.42 (4) Å3T = 350 K
Z = 2Prismatic
F(000) = 7680.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.030
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.6°, θmin = 3.7°
Tmin = 0.7, Tmax = 0.8h = 109
9486 measured reflectionsk = 910
701 independent reflectionsl = 3466
459 reflections with I > 2σ(I)
Refinement top
Refinement on F217 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.010 w = 1/[σ2(Fo2) + (0.0114P)2 + 0.365P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.024(Δ/σ)max < 0.001
S = 1.01Δρmax = 0.64 e Å3
701 reflectionsΔρmin = 0.46 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.25000.01230 (2)
Mg20.00000.00000.00000.00981 (8)
O30.1288 (3)0.8363 (3)0.12909 (2)0.02438 (18)
C40.00000.00000.13033 (3)0.01030 (12)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.01078 (3)0.01078 (3)0.01534 (4)0.00539 (1)0.0000.000
Mg20.00841 (11)0.00841 (11)0.01260 (19)0.00420 (6)0.0000.000
O30.0347 (6)0.0286 (5)0.0248 (2)0.0270 (4)0.0110 (5)0.0070 (4)
C40.00994 (19)0.00994 (19)0.0110 (3)0.00497 (9)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.8724 (13)Mg2—O3xviii2.0588 (7)
Ba1—O3ii2.8724 (13)Mg2—Ba1xix4.0251 (1)
Ba1—O3iii2.8724 (13)Mg2—Ba1xx4.0251 (1)
Ba1—O3iv2.8724 (13)Mg2—Ba1xxi4.0251 (1)
Ba1—O3v2.8724 (13)Mg2—Ba1xxii4.0251 (1)
Ba1—O3vi2.8724 (13)Mg2—Ba1xxiii4.0251 (1)
Ba1—O3vii3.0216 (14)Mg2—Ba1i4.0251 (1)
Ba1—O3viii3.0216 (14)O3—C4xxiv1.2756 (7)
Ba1—O3ix3.0216 (14)O3—Mg2xxv2.0588 (7)
Ba1—O3x3.0216 (14)O3—Ba1i2.8724 (13)
Ba1—O3xi3.0216 (14)O3—Ba1x3.0216 (14)
Ba1—O3xii3.0216 (14)C4—O3xxvi1.2756 (7)
Mg2—O3xiii2.0587 (7)C4—O3xxvii1.2756 (7)
Mg2—O3xiv2.0587 (7)C4—O3xxviii1.2756 (7)
Mg2—O3xv2.0587 (7)C4—Ba1xxii3.2985 (5)
Mg2—O3xvi2.0587 (7)C4—Ba1xx3.2985 (5)
Mg2—O3xvii2.0588 (7)C4—Ba1i3.2985 (5)
O3i—Ba1—O3ii136.79 (3)O3xiv—Mg2—O3xviii86.48 (3)
O3i—Ba1—O3iii123.27 (3)O3xv—Mg2—O3xviii93.52 (3)
O3ii—Ba1—O3iii94.16 (3)O3xvi—Mg2—O3xviii86.48 (3)
O3i—Ba1—O3iv65.02 (4)O3xvii—Mg2—O3xviii180.00 (7)
O3ii—Ba1—O3iv94.16 (3)O3xiii—Mg2—Ba1xix98.29 (2)
O3iii—Ba1—O3iv94.16 (3)O3xiv—Mg2—Ba1xix81.71 (2)
O3i—Ba1—O3v94.16 (3)O3xv—Mg2—Ba1xix42.66 (4)
O3ii—Ba1—O3v123.27 (3)O3xvi—Mg2—Ba1xix137.34 (4)
O3iii—Ba1—O3v65.02 (4)O3xvii—Mg2—Ba1xix46.97 (4)
O3iv—Ba1—O3v136.79 (3)O3xviii—Mg2—Ba1xix133.03 (4)
O3i—Ba1—O3vi94.16 (3)O3xiii—Mg2—Ba1xx81.71 (2)
O3ii—Ba1—O3vi65.02 (4)O3xiv—Mg2—Ba1xx98.29 (2)
O3iii—Ba1—O3vi136.79 (3)O3xv—Mg2—Ba1xx137.34 (4)
O3iv—Ba1—O3vi123.27 (3)O3xvi—Mg2—Ba1xx42.66 (4)
O3v—Ba1—O3vi94.16 (3)O3xvii—Mg2—Ba1xx133.03 (4)
O3i—Ba1—O3vii178.21 (3)O3xviii—Mg2—Ba1xx46.97 (4)
O3ii—Ba1—O3vii43.92 (3)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii57.12 (3)O3xiii—Mg2—Ba1xxi46.97 (4)
O3iv—Ba1—O3vii116.77 (3)O3xiv—Mg2—Ba1xxi133.03 (4)
O3v—Ba1—O3vii84.467 (17)O3xv—Mg2—Ba1xxi98.29 (2)
O3vi—Ba1—O3vii84.823 (18)O3xvi—Mg2—Ba1xxi81.71 (2)
O3i—Ba1—O3viii43.92 (3)O3xvii—Mg2—Ba1xxi42.66 (4)
O3ii—Ba1—O3viii178.21 (3)O3xviii—Mg2—Ba1xxi137.34 (4)
O3iii—Ba1—O3viii84.467 (17)Ba1xix—Mg2—Ba1xxi77.154 (1)
O3iv—Ba1—O3viii84.823 (17)Ba1xx—Mg2—Ba1xxi102.846 (1)
O3v—Ba1—O3viii57.12 (3)O3xiii—Mg2—Ba1xxii133.03 (4)
O3vi—Ba1—O3viii116.77 (3)O3xiv—Mg2—Ba1xxii46.97 (4)
O3vii—Ba1—O3viii135.45 (3)O3xv—Mg2—Ba1xxii81.71 (2)
O3i—Ba1—O3ix57.12 (3)O3xvi—Mg2—Ba1xxii98.29 (2)
O3ii—Ba1—O3ix84.823 (17)O3xvii—Mg2—Ba1xxii137.34 (4)
O3iii—Ba1—O3ix178.21 (3)O3xviii—Mg2—Ba1xxii42.66 (4)
O3iv—Ba1—O3ix84.467 (17)Ba1xix—Mg2—Ba1xxii102.846 (1)
O3v—Ba1—O3ix116.77 (3)Ba1xx—Mg2—Ba1xxii77.154 (1)
O3vi—Ba1—O3ix43.92 (3)Ba1xxi—Mg2—Ba1xxii180.0
O3vii—Ba1—O3ix122.55 (3)O3xiii—Mg2—Ba1xxiii42.66 (4)
O3viii—Ba1—O3ix96.53 (2)O3xiv—Mg2—Ba1xxiii137.34 (4)
O3i—Ba1—O3x116.77 (3)O3xv—Mg2—Ba1xxiii46.97 (4)
O3ii—Ba1—O3x84.467 (17)O3xvi—Mg2—Ba1xxiii133.03 (4)
O3iii—Ba1—O3x84.823 (17)O3xvii—Mg2—Ba1xxiii98.30 (2)
O3iv—Ba1—O3x178.21 (3)O3xviii—Mg2—Ba1xxiii81.70 (2)
O3v—Ba1—O3x43.92 (3)Ba1xix—Mg2—Ba1xxiii77.154 (2)
O3vi—Ba1—O3x57.12 (3)Ba1xx—Mg2—Ba1xxiii102.846 (2)
O3vii—Ba1—O3x61.45 (4)Ba1xxi—Mg2—Ba1xxiii77.154 (2)
O3viii—Ba1—O3x96.53 (2)Ba1xxii—Mg2—Ba1xxiii102.846 (1)
O3ix—Ba1—O3x96.53 (2)O3xiii—Mg2—Ba1i137.34 (4)
O3i—Ba1—O3xi84.823 (17)O3xiv—Mg2—Ba1i42.66 (4)
O3ii—Ba1—O3xi57.12 (3)O3xv—Mg2—Ba1i133.03 (4)
O3iii—Ba1—O3xi116.77 (3)O3xvi—Mg2—Ba1i46.97 (4)
O3iv—Ba1—O3xi43.92 (3)O3xvii—Mg2—Ba1i81.70 (2)
O3v—Ba1—O3xi178.21 (3)O3xviii—Mg2—Ba1i98.30 (2)
O3vi—Ba1—O3xi84.467 (17)Ba1xix—Mg2—Ba1i102.846 (2)
O3vii—Ba1—O3xi96.53 (2)Ba1xx—Mg2—Ba1i77.154 (2)
O3viii—Ba1—O3xi122.55 (3)Ba1xxi—Mg2—Ba1i102.846 (1)
O3ix—Ba1—O3xi61.45 (4)Ba1xxii—Mg2—Ba1i77.154 (2)
O3x—Ba1—O3xi135.45 (3)Ba1xxiii—Mg2—Ba1i180.0
O3i—Ba1—O3xii84.467 (17)C4xxiv—O3—Mg2xxv139.89 (7)
O3ii—Ba1—O3xii116.77 (3)C4xxiv—O3—Ba1i97.86 (7)
O3iii—Ba1—O3xii43.92 (3)Mg2xxv—O3—Ba1i108.29 (5)
O3iv—Ba1—O3xii57.12 (3)C4xxiv—O3—Ba1x90.91 (7)
O3v—Ba1—O3xii84.823 (17)Mg2xxv—O3—Ba1x103.15 (5)
O3vi—Ba1—O3xii178.21 (3)Ba1i—O3—Ba1x116.77 (3)
O3vii—Ba1—O3xii96.53 (2)O3xxvi—C4—O3xxvii119.896 (7)
O3viii—Ba1—O3xii61.45 (4)O3xxvi—C4—O3xxviii119.896 (7)
O3ix—Ba1—O3xii135.45 (3)O3xxvii—C4—O3xxviii119.893 (7)
O3x—Ba1—O3xii122.55 (3)O3xxvi—C4—Ba1xxii59.61 (6)
O3xi—Ba1—O3xii96.53 (2)O3xxvii—C4—Ba1xxii149.38 (7)
O3xiii—Mg2—O3xiv180.00 (9)O3xxviii—C4—Ba1xxii66.34 (6)
O3xiii—Mg2—O3xv86.49 (3)O3xxvi—C4—Ba1xx66.34 (7)
O3xiv—Mg2—O3xv93.51 (3)O3xxvii—C4—Ba1xx59.61 (6)
O3xiii—Mg2—O3xvi93.51 (3)O3xxviii—C4—Ba1xx149.38 (7)
O3xiv—Mg2—O3xvi86.49 (3)Ba1xxii—C4—Ba1xx99.090 (19)
O3xv—Mg2—O3xvi180.00 (9)O3xxvi—C4—Ba1i149.38 (7)
O3xiii—Mg2—O3xvii86.48 (3)O3xxvii—C4—Ba1i66.34 (6)
O3xiv—Mg2—O3xvii93.52 (3)O3xxviii—C4—Ba1i59.61 (6)
O3xv—Mg2—O3xvii86.48 (3)Ba1xxii—C4—Ba1i99.090 (19)
O3xvi—Mg2—O3xvii93.52 (3)Ba1xx—C4—Ba1i99.090 (19)
O3xiii—Mg2—O3xviii93.52 (3)
Symmetry codes: (i) x1/3, y+1/3, z+1/3; (ii) x+y2/3, y1/3, z+1/6; (iii) x+1/3, xy+2/3, z+1/6; (iv) y+1/3, x1/3, z+1/6; (v) y1/3, x+y2/3, z+1/3; (vi) xy+2/3, x+1/3, z+1/3; (vii) y+4/3, x+2/3, z+1/6; (viii) xy+2/3, x2/3, z+1/3; (ix) y4/3, x+y2/3, z+1/3; (x) x+2/3, y+4/3, z+1/3; (xi) x2/3, xy+2/3, z+1/6; (xii) x+y2/3, y4/3, z+1/6; (xiii) x+y1/3, y2/3, z1/6; (xiv) xy+1/3, y+2/3, z+1/6; (xv) x1/3, xy+1/3, z1/6; (xvi) x+1/3, x+y1/3, z+1/6; (xvii) y+2/3, x+1/3, z1/6; (xviii) y2/3, x1/3, z+1/6; (xix) x2/3, y1/3, z1/3; (xx) x+2/3, y+1/3, z+1/3; (xxi) x+1/3, y+2/3, z1/3; (xxii) x1/3, y2/3, z+1/3; (xxiii) x+1/3, y1/3, z1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, z+1/6; (xxvi) x, y1, z; (xxvii) y+1, xy+1, z; (xxviii) x+y1, x, z.
(norse_360) top
Crystal data top
C6Ba3Mg3O18Dx = 3.834 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 5541 reflections
a = 5.0206 (1) Åθ = 1.5–45°
c = 33.5307 (14) ŵ = 8.22 mm1
V = 731.95 (4) Å3T = 360 K
Z = 2Prismatic
F(000) = 7680.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.027
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.6°, θmin = 3.7°
Tmin = 0.7, Tmax = 0.8h = 108
5541 measured reflectionsk = 810
701 independent reflectionsl = 3466
444 reflections with I > 2σ(I)
Refinement top
Refinement on F217 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.012 w = 1/[σ2(Fo2) + (0.0128P)2 + 0.6467P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.028(Δ/σ)max < 0.001
S = 0.99Δρmax = 0.76 e Å3
701 reflectionsΔρmin = 0.72 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.25000.01269 (3)
Mg20.00000.00000.00000.01003 (9)
O30.1326 (4)0.8401 (4)0.12905 (3)0.0253 (2)
C40.00000.00000.13031 (4)0.01021 (15)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.01117 (3)0.01117 (3)0.01572 (5)0.00558 (2)0.0000.000
Mg20.00870 (14)0.00870 (14)0.0127 (2)0.00435 (7)0.0000.000
O30.0359 (8)0.0301 (6)0.0256 (3)0.0282 (5)0.0121 (7)0.0077 (6)
C40.0099 (2)0.0099 (2)0.0109 (4)0.00493 (11)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.8884 (19)Mg2—O3xviii2.0595 (8)
Ba1—O3ii2.8884 (19)Mg2—Ba1xix4.0262 (1)
Ba1—O3iii2.8884 (19)Mg2—Ba1xx4.0262 (1)
Ba1—O3iv2.8884 (19)Mg2—Ba1xxi4.0262 (1)
Ba1—O3v2.8884 (19)Mg2—Ba1xxii4.0262 (1)
Ba1—O3vi2.8884 (19)Mg2—Ba1iii4.0262 (1)
Ba1—O3vii3.005 (2)Mg2—Ba1xxiii4.0262 (1)
Ba1—O3viii3.005 (2)O3—C4xxiv1.2747 (8)
Ba1—O3ix3.005 (2)O3—Mg2xxv2.0595 (8)
Ba1—O3x3.005 (2)O3—Ba1iii2.8884 (19)
Ba1—O3xi3.005 (2)O3—Ba1x3.005 (2)
Ba1—O3xii3.005 (2)C4—O3xxvi1.2747 (8)
Mg2—O3xiii2.0595 (8)C4—O3xxvii1.2747 (8)
Mg2—O3xiv2.0595 (8)C4—O3xxviii1.2747 (8)
Mg2—O3xv2.0595 (8)C4—Ba1xxii3.2990 (6)
Mg2—O3xvi2.0595 (8)C4—Ba1xx3.2990 (6)
Mg2—O3xvii2.0595 (8)C4—Ba1iii3.2990 (6)
O3i—Ba1—O3ii123.17 (3)O3xiv—Mg2—O3xviii86.40 (4)
O3i—Ba1—O3iii136.62 (4)O3xv—Mg2—O3xviii93.60 (4)
O3ii—Ba1—O3iii94.46 (4)O3xvi—Mg2—O3xviii86.40 (4)
O3i—Ba1—O3iv94.46 (4)O3xvii—Mg2—O3xviii180.00 (9)
O3ii—Ba1—O3iv136.62 (4)O3xiii—Mg2—Ba1xix43.10 (5)
O3iii—Ba1—O3iv64.57 (6)O3xiv—Mg2—Ba1xix136.90 (5)
O3i—Ba1—O3v94.46 (4)O3xv—Mg2—Ba1xix98.25 (3)
O3ii—Ba1—O3v64.57 (6)O3xvi—Mg2—Ba1xix81.75 (3)
O3iii—Ba1—O3v123.17 (3)O3xvii—Mg2—Ba1xix46.48 (6)
O3iv—Ba1—O3v94.45 (4)O3xviii—Mg2—Ba1xix133.52 (6)
O3i—Ba1—O3vi64.57 (6)O3xiii—Mg2—Ba1xx136.90 (5)
O3ii—Ba1—O3vi94.46 (4)O3xiv—Mg2—Ba1xx43.10 (5)
O3iii—Ba1—O3vi94.45 (4)O3xv—Mg2—Ba1xx81.75 (3)
O3iv—Ba1—O3vi123.17 (3)O3xvi—Mg2—Ba1xx98.25 (3)
O3v—Ba1—O3vi136.62 (4)O3xvii—Mg2—Ba1xx133.52 (6)
O3i—Ba1—O3vii178.61 (4)O3xviii—Mg2—Ba1xx46.48 (6)
O3ii—Ba1—O3vii57.13 (3)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii43.92 (3)O3xiii—Mg2—Ba1xxi98.25 (3)
O3iv—Ba1—O3vii84.75 (2)O3xiv—Mg2—Ba1xxi81.75 (3)
O3v—Ba1—O3vii84.47 (2)O3xv—Mg2—Ba1xxi46.47 (6)
O3vi—Ba1—O3vii116.82 (3)O3xvi—Mg2—Ba1xxi133.53 (6)
O3i—Ba1—O3viii57.13 (3)O3xvii—Mg2—Ba1xxi43.10 (5)
O3ii—Ba1—O3viii178.61 (4)O3xviii—Mg2—Ba1xxi136.90 (5)
O3iii—Ba1—O3viii84.75 (2)Ba1xix—Mg2—Ba1xxi77.143 (2)
O3iv—Ba1—O3viii43.92 (3)Ba1xx—Mg2—Ba1xxi102.857 (2)
O3v—Ba1—O3viii116.82 (3)O3xiii—Mg2—Ba1xxii81.75 (3)
O3vi—Ba1—O3viii84.47 (2)O3xiv—Mg2—Ba1xxii98.25 (3)
O3vii—Ba1—O3viii122.61 (3)O3xv—Mg2—Ba1xxii133.53 (6)
O3i—Ba1—O3ix43.92 (3)O3xvi—Mg2—Ba1xxii46.47 (6)
O3ii—Ba1—O3ix84.47 (2)O3xvii—Mg2—Ba1xxii136.90 (5)
O3iii—Ba1—O3ix178.61 (5)O3xviii—Mg2—Ba1xxii43.10 (5)
O3iv—Ba1—O3ix116.82 (3)Ba1xix—Mg2—Ba1xxii102.857 (2)
O3v—Ba1—O3ix57.13 (3)Ba1xx—Mg2—Ba1xxii77.143 (2)
O3vi—Ba1—O3ix84.75 (2)Ba1xxi—Mg2—Ba1xxii180.0
O3vii—Ba1—O3ix135.58 (3)O3xiii—Mg2—Ba1iii133.52 (6)
O3viii—Ba1—O3ix96.31 (3)O3xiv—Mg2—Ba1iii46.48 (6)
O3i—Ba1—O3x84.47 (2)O3xv—Mg2—Ba1iii136.90 (5)
O3ii—Ba1—O3x43.92 (3)O3xvi—Mg2—Ba1iii43.10 (5)
O3iii—Ba1—O3x116.82 (3)O3xvii—Mg2—Ba1iii81.75 (3)
O3iv—Ba1—O3x178.61 (5)O3xviii—Mg2—Ba1iii98.25 (3)
O3v—Ba1—O3x84.75 (2)Ba1xix—Mg2—Ba1iii102.857 (2)
O3vi—Ba1—O3x57.13 (3)Ba1xx—Mg2—Ba1iii77.143 (2)
O3vii—Ba1—O3x96.31 (3)Ba1xxi—Mg2—Ba1iii102.857 (2)
O3viii—Ba1—O3x135.58 (3)Ba1xxii—Mg2—Ba1iii77.143 (2)
O3ix—Ba1—O3x61.78 (5)O3xiii—Mg2—Ba1xxiii46.48 (6)
O3i—Ba1—O3xi84.75 (2)O3xiv—Mg2—Ba1xxiii133.52 (6)
O3ii—Ba1—O3xi116.82 (3)O3xv—Mg2—Ba1xxiii43.10 (5)
O3iii—Ba1—O3xi57.13 (3)O3xvi—Mg2—Ba1xxiii136.90 (5)
O3iv—Ba1—O3xi84.47 (2)O3xvii—Mg2—Ba1xxiii98.25 (3)
O3v—Ba1—O3xi178.61 (4)O3xviii—Mg2—Ba1xxiii81.75 (3)
O3vi—Ba1—O3xi43.92 (3)Ba1xix—Mg2—Ba1xxiii77.143 (2)
O3vii—Ba1—O3xi96.31 (3)Ba1xx—Mg2—Ba1xxiii102.857 (2)
O3viii—Ba1—O3xi61.78 (5)Ba1xxi—Mg2—Ba1xxiii77.143 (2)
O3ix—Ba1—O3xi122.61 (3)Ba1xxii—Mg2—Ba1xxiii102.857 (2)
O3x—Ba1—O3xi96.31 (3)Ba1iii—Mg2—Ba1xxiii180.0
O3i—Ba1—O3xii116.82 (3)C4xxiv—O3—Mg2xxv139.99 (8)
O3ii—Ba1—O3xii84.75 (2)C4xxiv—O3—Ba1iii97.15 (9)
O3iii—Ba1—O3xii84.47 (2)Mg2xxv—O3—Ba1iii107.74 (7)
O3iv—Ba1—O3xii57.13 (3)C4xxiv—O3—Ba1x91.71 (10)
O3v—Ba1—O3xii43.92 (3)Mg2xxv—O3—Ba1x103.73 (7)
O3vi—Ba1—O3xii178.61 (4)Ba1iii—O3—Ba1x116.82 (3)
O3vii—Ba1—O3xii61.78 (5)O3xxvi—C4—O3xxvii119.889 (8)
O3viii—Ba1—O3xii96.31 (3)O3xxvi—C4—O3xxviii119.889 (8)
O3ix—Ba1—O3xii96.31 (3)O3xxvii—C4—O3xxviii119.889 (9)
O3x—Ba1—O3xii122.61 (3)O3xxvi—C4—Ba1xxii65.57 (9)
O3xi—Ba1—O3xii135.58 (3)O3xxvii—C4—Ba1xxii149.42 (8)
O3xiii—Mg2—O3xiv180.00 (14)O3xxviii—C4—Ba1xxii60.31 (9)
O3xiii—Mg2—O3xv86.40 (4)O3xxvi—C4—Ba1xx149.42 (8)
O3xiv—Mg2—O3xv93.60 (4)O3xxvii—C4—Ba1xx60.31 (9)
O3xiii—Mg2—O3xvi93.60 (4)O3xxviii—C4—Ba1xx65.57 (9)
O3xiv—Mg2—O3xvi86.40 (4)Ba1xxii—C4—Ba1xx99.09 (2)
O3xv—Mg2—O3xvi180.00 (13)O3xxvi—C4—Ba1iii60.31 (9)
O3xiii—Mg2—O3xvii86.40 (4)O3xxvii—C4—Ba1iii65.57 (9)
O3xiv—Mg2—O3xvii93.60 (4)O3xxviii—C4—Ba1iii149.42 (8)
O3xv—Mg2—O3xvii86.40 (4)Ba1xxii—C4—Ba1iii99.09 (2)
O3xvi—Mg2—O3xvii93.60 (4)Ba1xx—C4—Ba1iii99.09 (2)
O3xiii—Mg2—O3xviii93.60 (4)
Symmetry codes: (i) x+y2/3, y1/3, z+1/6; (ii) y1/3, x+y2/3, z+1/3; (iii) x1/3, y+1/3, z+1/3; (iv) y+1/3, x1/3, z+1/6; (v) x+1/3, xy+2/3, z+1/6; (vi) xy+2/3, x+1/3, z+1/3; (vii) xy+2/3, x2/3, z+1/3; (viii) x2/3, xy+2/3, z+1/6; (ix) y+4/3, x+2/3, z+1/6; (x) x+2/3, y+4/3, z+1/3; (xi) y4/3, x+y2/3, z+1/3; (xii) x+y2/3, y4/3, z+1/6; (xiii) x1/3, xy+1/3, z1/6; (xiv) x+1/3, x+y1/3, z+1/6; (xv) x+y1/3, y2/3, z1/6; (xvi) xy+1/3, y+2/3, z+1/6; (xvii) y+2/3, x+1/3, z1/6; (xviii) y2/3, x1/3, z+1/6; (xix) x2/3, y1/3, z1/3; (xx) x+2/3, y+1/3, z+1/3; (xxi) x+1/3, y+2/3, z1/3; (xxii) x1/3, y2/3, z+1/3; (xxiii) x+1/3, y1/3, z1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, z+1/6; (xxvi) x+y1, x, z; (xxvii) y+1, xy+1, z; (xxviii) x, y1, z.
(norse_370) top
Crystal data top
C6Ba3Mg3O18Dx = 3.837 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3mCell parameters from 5014 reflections
a = 5.0209 (1) Åθ = 1.5–45°
c = 16.7515 (5) ŵ = 8.23 mm1
V = 365.72 (2) Å3T = 370 K
Z = 1Prismatic
F(000) = 3840.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.026
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.6°, θmin = 3.7°
Tmin = 0.7, Tmax = 0.8h = 910
5014 measured reflectionsk = 109
428 independent reflectionsl = 1733
428 reflections with I > 2σ(I)
Refinement top
Refinement on F214 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.014 w = 1/[σ2(Fo2) + (0.0123P)2 + 0.8639P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.033(Δ/σ)max < 0.001
S = 1.17Δρmax = 1.12 e Å3
428 reflectionsΔρmin = 0.72 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.50000.01328 (4)
Mg20.00000.00000.00000.01049 (15)
O30.85354 (13)0.7071 (3)0.25778 (8)0.0267 (2)
C40.00000.00000.26072 (11)0.0109 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.01148 (5)0.01148 (5)0.01687 (7)0.00574 (2)0.0000.000
Mg20.0088 (2)0.0088 (2)0.0138 (4)0.00441 (11)0.0000.000
O30.0351 (5)0.0097 (3)0.0269 (5)0.00484 (17)0.00210 (16)0.0042 (3)
C40.0105 (4)0.0105 (4)0.0116 (5)0.00525 (18)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.9433 (7)Mg2—O3xviii2.0598 (11)
Ba1—O3ii2.9433 (7)Mg2—Ba1xix4.0246 (1)
Ba1—O3iii2.9433 (7)Mg2—Ba1xx4.0246 (1)
Ba1—O3iv2.9433 (7)Mg2—Ba1xvi4.0246 (1)
Ba1—O3v2.9433 (7)Mg2—Ba1xxi4.0246 (1)
Ba1—O3vi2.9433 (7)Mg2—Ba1xxii4.0247 (1)
Ba1—O3vii2.9433 (7)Mg2—Ba1xxiii4.0247 (1)
Ba1—O3viii2.9433 (7)O3—C4xxiv1.2747 (11)
Ba1—O3ix2.9433 (7)O3—Mg2xxv2.0598 (11)
Ba1—O3x2.9433 (7)O3—Ba1xix2.9433 (7)
Ba1—O3xi2.9433 (7)O3—Ba1xxvi2.9433 (7)
Ba1—O3xii2.9433 (7)C4—O3xxvii1.2746 (11)
Mg2—O3xiii2.0598 (11)C4—O3xxviii1.2746 (11)
Mg2—O3xiv2.0598 (11)C4—O3xxix1.2746 (11)
Mg2—O3xv2.0598 (11)C4—Ba1xvi3.2993 (9)
Mg2—O3xvi2.0598 (11)C4—Ba1xix3.2993 (9)
Mg2—O3xvii2.0598 (11)C4—Ba1xxii3.2993 (9)
O3i—Ba1—O3ii180.0O3xiv—Mg2—O3xviii86.20 (5)
O3i—Ba1—O3iii57.13 (4)O3xv—Mg2—O3xviii93.80 (5)
O3ii—Ba1—O3iii122.87 (4)O3xvi—Mg2—O3xviii86.20 (5)
O3i—Ba1—O3iv122.87 (4)O3xvii—Mg2—O3xviii180.00 (6)
O3ii—Ba1—O3iv57.13 (4)O3xiii—Mg2—Ba1xix44.734 (17)
O3iii—Ba1—O3iv180.0O3xiv—Mg2—Ba1xix135.266 (17)
O3i—Ba1—O3v44.02 (4)O3xv—Mg2—Ba1xix98.17 (4)
O3ii—Ba1—O3v135.98 (4)O3xvi—Mg2—Ba1xix81.83 (4)
O3iii—Ba1—O3v95.54 (3)O3xvii—Mg2—Ba1xix44.736 (17)
O3iv—Ba1—O3v84.46 (3)O3xviii—Mg2—Ba1xix135.264 (17)
O3i—Ba1—O3vi135.98 (4)O3xiii—Mg2—Ba1xx135.266 (17)
O3ii—Ba1—O3vi44.02 (4)O3xiv—Mg2—Ba1xx44.734 (17)
O3iii—Ba1—O3vi84.46 (3)O3xv—Mg2—Ba1xx81.83 (4)
O3iv—Ba1—O3vi95.54 (3)O3xvi—Mg2—Ba1xx98.17 (4)
O3v—Ba1—O3vi180.0O3xvii—Mg2—Ba1xx135.264 (17)
O3i—Ba1—O3vii95.54 (3)O3xviii—Mg2—Ba1xx44.736 (17)
O3ii—Ba1—O3vii84.46 (3)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii44.02 (4)O3xiii—Mg2—Ba1xvi98.17 (4)
O3iv—Ba1—O3vii135.98 (4)O3xiv—Mg2—Ba1xvi81.83 (4)
O3v—Ba1—O3vii117.07 (4)O3xv—Mg2—Ba1xvi44.734 (17)
O3vi—Ba1—O3vii62.93 (4)O3xvi—Mg2—Ba1xvi135.266 (17)
O3i—Ba1—O3viii84.46 (3)O3xvii—Mg2—Ba1xvi44.736 (17)
O3ii—Ba1—O3viii95.54 (3)O3xviii—Mg2—Ba1xvi135.264 (17)
O3iii—Ba1—O3viii135.98 (4)Ba1xix—Mg2—Ba1xvi77.184 (2)
O3iv—Ba1—O3viii44.02 (4)Ba1xx—Mg2—Ba1xvi102.816 (2)
O3v—Ba1—O3viii62.93 (4)O3xiii—Mg2—Ba1xxi81.83 (4)
O3vi—Ba1—O3viii117.07 (4)O3xiv—Mg2—Ba1xxi98.17 (4)
O3vii—Ba1—O3viii180.00 (2)O3xv—Mg2—Ba1xxi135.266 (17)
O3i—Ba1—O3ix95.54 (3)O3xvi—Mg2—Ba1xxi44.734 (17)
O3ii—Ba1—O3ix84.46 (3)O3xvii—Mg2—Ba1xxi135.264 (17)
O3iii—Ba1—O3ix117.07 (4)O3xviii—Mg2—Ba1xxi44.736 (17)
O3iv—Ba1—O3ix62.93 (4)Ba1xix—Mg2—Ba1xxi102.816 (2)
O3v—Ba1—O3ix57.13 (4)Ba1xx—Mg2—Ba1xxi77.184 (2)
O3vi—Ba1—O3ix122.87 (4)Ba1xvi—Mg2—Ba1xxi180.0
O3vii—Ba1—O3ix95.54 (3)O3xiii—Mg2—Ba1xxii44.736 (17)
O3viii—Ba1—O3ix84.46 (3)O3xiv—Mg2—Ba1xxii135.264 (17)
O3i—Ba1—O3x84.46 (3)O3xv—Mg2—Ba1xxii44.736 (17)
O3ii—Ba1—O3x95.54 (3)O3xvi—Mg2—Ba1xxii135.264 (17)
O3iii—Ba1—O3x62.93 (4)O3xvii—Mg2—Ba1xxii98.17 (4)
O3iv—Ba1—O3x117.07 (4)O3xviii—Mg2—Ba1xxii81.83 (4)
O3v—Ba1—O3x122.87 (4)Ba1xix—Mg2—Ba1xxii77.184 (1)
O3vi—Ba1—O3x57.13 (4)Ba1xx—Mg2—Ba1xxii102.816 (2)
O3vii—Ba1—O3x84.46 (3)Ba1xvi—Mg2—Ba1xxii77.184 (2)
O3viii—Ba1—O3x95.54 (3)Ba1xxi—Mg2—Ba1xxii102.816 (2)
O3ix—Ba1—O3x180.0O3xiii—Mg2—Ba1xxiii135.264 (17)
O3i—Ba1—O3xi62.93 (4)O3xiv—Mg2—Ba1xxiii44.736 (17)
O3ii—Ba1—O3xi117.07 (4)O3xv—Mg2—Ba1xxiii135.264 (17)
O3iii—Ba1—O3xi84.46 (3)O3xvi—Mg2—Ba1xxiii44.736 (17)
O3iv—Ba1—O3xi95.54 (3)O3xvii—Mg2—Ba1xxiii81.83 (4)
O3v—Ba1—O3xi84.46 (3)O3xviii—Mg2—Ba1xxiii98.17 (4)
O3vi—Ba1—O3xi95.54 (3)Ba1xix—Mg2—Ba1xxiii102.816 (2)
O3vii—Ba1—O3xi122.87 (4)Ba1xx—Mg2—Ba1xxiii77.184 (1)
O3viii—Ba1—O3xi57.13 (4)Ba1xvi—Mg2—Ba1xxiii102.816 (2)
O3ix—Ba1—O3xi135.98 (5)Ba1xxi—Mg2—Ba1xxiii77.184 (2)
O3x—Ba1—O3xi44.02 (4)Ba1xxii—Mg2—Ba1xxiii180.0
O3i—Ba1—O3xii117.07 (4)C4xxiv—O3—Mg2xxv139.88 (12)
O3ii—Ba1—O3xii62.93 (4)C4xxiv—O3—Ba1xix94.57 (5)
O3iii—Ba1—O3xii95.54 (3)Mg2xxv—O3—Ba1xix105.76 (3)
O3iv—Ba1—O3xii84.46 (3)C4xxiv—O3—Ba1xxvi94.57 (5)
O3v—Ba1—O3xii95.54 (3)Mg2xxv—O3—Ba1xxvi105.76 (3)
O3vi—Ba1—O3xii84.46 (3)Ba1xix—O3—Ba1xxvi117.06 (4)
O3vii—Ba1—O3xii57.13 (4)O3xxvii—C4—O3xxviii119.852 (14)
O3viii—Ba1—O3xii122.87 (4)O3xxvii—C4—O3xxix119.852 (14)
O3ix—Ba1—O3xii44.02 (4)O3xxviii—C4—O3xxix119.852 (14)
O3x—Ba1—O3xii135.98 (5)O3xxvii—C4—Ba1xvi62.78 (5)
O3xi—Ba1—O3xii180.0O3xxviii—C4—Ba1xvi149.26 (12)
O3xiii—Mg2—O3xiv180.00 (6)O3xxix—C4—Ba1xvi62.78 (5)
O3xiii—Mg2—O3xv86.20 (5)O3xxvii—C4—Ba1xix149.26 (12)
O3xiv—Mg2—O3xv93.80 (5)O3xxviii—C4—Ba1xix62.78 (5)
O3xiii—Mg2—O3xvi93.80 (5)O3xxix—C4—Ba1xix62.78 (5)
O3xiv—Mg2—O3xvi86.20 (5)Ba1xvi—C4—Ba1xix99.09 (4)
O3xv—Mg2—O3xvi180.00 (7)O3xxvii—C4—Ba1xxii62.78 (5)
O3xiii—Mg2—O3xvii86.20 (5)O3xxviii—C4—Ba1xxii62.78 (5)
O3xiv—Mg2—O3xvii93.80 (5)O3xxix—C4—Ba1xxii149.26 (12)
O3xv—Mg2—O3xvii86.20 (5)Ba1xvi—C4—Ba1xxii99.09 (4)
O3xvi—Mg2—O3xvii93.80 (5)Ba1xix—C4—Ba1xxii99.09 (4)
O3xiii—Mg2—O3xviii93.80 (5)
Symmetry codes: (i) x+1/3, y+2/3, z+2/3; (ii) x1/3, y2/3, z+1/3; (iii) y2/3, x+y+2/3, z+2/3; (iv) y+2/3, xy2/3, z+1/3; (v) xy2/3, x4/3, z+2/3; (vi) x+y+2/3, x+4/3, z+1/3; (vii) xy+1/3, x1/3, z+2/3; (viii) x+y1/3, x+1/3, z+1/3; (ix) y2/3, x+y1/3, z+2/3; (x) y+2/3, xy+1/3, z+1/3; (xi) x4/3, y2/3, z+1/3; (xii) x+4/3, y+2/3, z+2/3; (xiii) y1/3, x+y+1/3, z+1/3; (xiv) y+1/3, xy1/3, z1/3; (xv) x+2/3, y+1/3, z+1/3; (xvi) x2/3, y1/3, z1/3; (xvii) xy1/3, x2/3, z+1/3; (xviii) x+y+1/3, x+2/3, z1/3; (xix) x+1/3, y+2/3, z1/3; (xx) x1/3, y2/3, z2/3; (xxi) x+2/3, y+1/3, z2/3; (xxii) x+1/3, y1/3, z1/3; (xxiii) x1/3, y+1/3, z2/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z1/3; (xxvii) x1, y1, z; (xxviii) y+1, xy, z; (xxix) x+y, x+1, z.
(norse_380) top
Crystal data top
C6Ba3Mg3O18Dx = 3.826 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3mCell parameters from 5028 reflections
a = 5.0214 (2) Åθ = 1.5–45°
c = 16.7931 (6) ŵ = 8.21 mm1
V = 366.70 (3) Å3T = 380 K
Z = 1Prismatic
F(000) = 3840.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.029
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.5°, θmin = 3.6°
Tmin = 0.7, Tmax = 0.8h = 910
5028 measured reflectionsk = 109
427 independent reflectionsl = 3217
427 reflections with I > 2σ(I)
Refinement top
Refinement on F214 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.015 w = 1/[σ2(Fo2) + (0.0098P)2 + 0.8518P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.030(Δ/σ)max < 0.001
S = 1.14Δρmax = 1.22 e Å3
427 reflectionsΔρmin = 0.56 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.50000.01337 (4)
Mg20.00000.00000.00000.01058 (14)
O30.85362 (12)0.7072 (2)0.25778 (7)0.0268 (2)
C40.00000.00000.26077 (10)0.0109 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.01179 (4)0.01179 (4)0.01654 (6)0.00590 (2)0.0000.000
Mg20.0090 (2)0.0090 (2)0.0137 (3)0.00450 (10)0.0000.000
O30.0356 (5)0.0100 (3)0.0263 (4)0.00499 (16)0.00209 (15)0.0042 (3)
C40.0107 (3)0.0107 (3)0.0113 (5)0.00533 (16)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.9455 (6)Mg2—O3xviii2.0625 (10)
Ba1—O3ii2.9455 (6)Mg2—Ba1xix4.0297 (1)
Ba1—O3iii2.9455 (6)Mg2—Ba1xx4.0297 (1)
Ba1—O3iv2.9455 (6)Mg2—Ba1xvi4.0297 (1)
Ba1—O3v2.9455 (6)Mg2—Ba1xxi4.0297 (1)
Ba1—O3vi2.9455 (6)Mg2—Ba1xxii4.0297 (1)
Ba1—O3vii2.9455 (6)Mg2—Ba1xxiii4.0297 (1)
Ba1—O3viii2.9455 (6)O3—C4xxiv1.2741 (11)
Ba1—O3ix2.9455 (6)O3—Mg2xxv2.0624 (10)
Ba1—O3x2.9455 (6)O3—Ba1xix2.9455 (6)
Ba1—O3xi2.9455 (6)O3—Ba1xxvi2.9456 (6)
Ba1—O3xii2.9455 (6)C4—O3xxvii1.2741 (11)
Mg2—O3xiii2.0624 (10)C4—O3xxviii1.2741 (11)
Mg2—O3xiv2.0624 (10)C4—O3xxix1.2741 (11)
Mg2—O3xv2.0624 (10)C4—Ba1xvi3.3019 (8)
Mg2—O3xvi2.0624 (10)C4—Ba1xix3.3019 (8)
Mg2—O3xvii2.0625 (10)C4—Ba1xxii3.3019 (8)
O3i—Ba1—O3ii180.0O3xiv—Mg2—O3xviii86.12 (5)
O3i—Ba1—O3iii43.96 (4)O3xv—Mg2—O3xviii93.88 (5)
O3ii—Ba1—O3iii136.04 (4)O3xvi—Mg2—O3xviii86.12 (5)
O3i—Ba1—O3iv136.04 (4)O3xvii—Mg2—O3xviii180.00 (5)
O3ii—Ba1—O3iv43.96 (4)O3xiii—Mg2—Ba1xix44.692 (15)
O3iii—Ba1—O3iv180.0O3xiv—Mg2—Ba1xix135.308 (15)
O3i—Ba1—O3v57.12 (4)O3xv—Mg2—Ba1xix98.04 (3)
O3ii—Ba1—O3v122.88 (4)O3xvi—Mg2—Ba1xix81.96 (3)
O3iii—Ba1—O3v95.46 (3)O3xvii—Mg2—Ba1xix44.694 (15)
O3iv—Ba1—O3v84.54 (3)O3xviii—Mg2—Ba1xix135.306 (15)
O3i—Ba1—O3vi122.88 (4)O3xiii—Mg2—Ba1xx135.308 (15)
O3ii—Ba1—O3vi57.12 (4)O3xiv—Mg2—Ba1xx44.692 (15)
O3iii—Ba1—O3vi84.54 (3)O3xv—Mg2—Ba1xx81.96 (3)
O3iv—Ba1—O3vi95.46 (3)O3xvi—Mg2—Ba1xx98.04 (3)
O3v—Ba1—O3vi180.00 (4)O3xvii—Mg2—Ba1xx135.306 (15)
O3i—Ba1—O3vii116.94 (4)O3xviii—Mg2—Ba1xx44.694 (15)
O3ii—Ba1—O3vii63.06 (4)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii95.46 (3)O3xiii—Mg2—Ba1xvi98.04 (3)
O3iv—Ba1—O3vii84.54 (3)O3xiv—Mg2—Ba1xvi81.96 (3)
O3v—Ba1—O3vii95.46 (3)O3xv—Mg2—Ba1xvi44.692 (15)
O3vi—Ba1—O3vii84.54 (3)O3xvi—Mg2—Ba1xvi135.308 (15)
O3i—Ba1—O3viii63.06 (4)O3xvii—Mg2—Ba1xvi44.694 (15)
O3ii—Ba1—O3viii116.94 (4)O3xviii—Mg2—Ba1xvi135.306 (15)
O3iii—Ba1—O3viii84.54 (3)Ba1xix—Mg2—Ba1xvi77.079 (2)
O3iv—Ba1—O3viii95.46 (3)Ba1xx—Mg2—Ba1xvi102.921 (2)
O3v—Ba1—O3viii84.54 (3)O3xiii—Mg2—Ba1xxi81.96 (3)
O3vi—Ba1—O3viii95.46 (3)O3xiv—Mg2—Ba1xxi98.04 (3)
O3vii—Ba1—O3viii180.0O3xv—Mg2—Ba1xxi135.308 (15)
O3i—Ba1—O3ix84.54 (3)O3xvi—Mg2—Ba1xxi44.692 (15)
O3ii—Ba1—O3ix95.46 (3)O3xvii—Mg2—Ba1xxi135.306 (15)
O3iii—Ba1—O3ix63.06 (4)O3xviii—Mg2—Ba1xxi44.694 (15)
O3iv—Ba1—O3ix116.94 (4)Ba1xix—Mg2—Ba1xxi102.921 (2)
O3v—Ba1—O3ix136.04 (4)Ba1xx—Mg2—Ba1xxi77.079 (2)
O3vi—Ba1—O3ix43.96 (4)Ba1xvi—Mg2—Ba1xxi180.0
O3vii—Ba1—O3ix122.88 (4)O3xiii—Mg2—Ba1xxii44.695 (15)
O3viii—Ba1—O3ix57.12 (4)O3xiv—Mg2—Ba1xxii135.305 (15)
O3i—Ba1—O3x95.46 (3)O3xv—Mg2—Ba1xxii44.695 (15)
O3ii—Ba1—O3x84.54 (3)O3xvi—Mg2—Ba1xxii135.305 (15)
O3iii—Ba1—O3x57.12 (4)O3xvii—Mg2—Ba1xxii98.04 (3)
O3iv—Ba1—O3x122.88 (4)O3xviii—Mg2—Ba1xxii81.96 (3)
O3v—Ba1—O3x116.94 (4)Ba1xix—Mg2—Ba1xxii77.079 (2)
O3vi—Ba1—O3x63.06 (4)Ba1xx—Mg2—Ba1xxii102.921 (2)
O3vii—Ba1—O3x43.96 (4)Ba1xvi—Mg2—Ba1xxii77.079 (2)
O3viii—Ba1—O3x136.04 (4)Ba1xxi—Mg2—Ba1xxii102.921 (2)
O3ix—Ba1—O3x84.54 (3)O3xiii—Mg2—Ba1xxiii135.305 (15)
O3i—Ba1—O3xi95.46 (3)O3xiv—Mg2—Ba1xxiii44.695 (15)
O3ii—Ba1—O3xi84.54 (3)O3xv—Mg2—Ba1xxiii135.305 (15)
O3iii—Ba1—O3xi116.94 (4)O3xvi—Mg2—Ba1xxiii44.695 (15)
O3iv—Ba1—O3xi63.06 (4)O3xvii—Mg2—Ba1xxiii81.96 (3)
O3v—Ba1—O3xi43.96 (4)O3xviii—Mg2—Ba1xxiii98.04 (3)
O3vi—Ba1—O3xi136.04 (4)Ba1xix—Mg2—Ba1xxiii102.921 (2)
O3vii—Ba1—O3xi57.12 (4)Ba1xx—Mg2—Ba1xxiii77.079 (2)
O3viii—Ba1—O3xi122.88 (4)Ba1xvi—Mg2—Ba1xxiii102.921 (2)
O3ix—Ba1—O3xi180.0Ba1xxi—Mg2—Ba1xxiii77.079 (2)
O3x—Ba1—O3xi95.46 (3)Ba1xxii—Mg2—Ba1xxiii180.0
O3i—Ba1—O3xii84.54 (3)C4xxiv—O3—Mg2xxv139.78 (11)
O3ii—Ba1—O3xii95.46 (3)C4xxiv—O3—Ba1xix94.61 (5)
O3iii—Ba1—O3xii122.88 (4)Mg2xxv—O3—Ba1xix105.80 (3)
O3iv—Ba1—O3xii57.12 (4)C4xxiv—O3—Ba1xxvi94.61 (5)
O3v—Ba1—O3xii63.06 (4)Mg2xxv—O3—Ba1xxvi105.80 (3)
O3vi—Ba1—O3xii116.94 (4)Ba1xix—O3—Ba1xxvi116.94 (4)
O3vii—Ba1—O3xii136.04 (4)O3xxvii—C4—O3xxviii119.847 (13)
O3viii—Ba1—O3xii43.96 (4)O3xxvii—C4—O3xxix119.847 (13)
O3ix—Ba1—O3xii95.46 (3)O3xxviii—C4—O3xxix119.844 (13)
O3x—Ba1—O3xii180.0O3xxvii—C4—Ba1xvi62.77 (4)
O3xi—Ba1—O3xii84.54 (3)O3xxviii—C4—Ba1xvi62.77 (4)
O3xiii—Mg2—O3xiv180.00 (5)O3xxix—C4—Ba1xvi149.14 (11)
O3xiii—Mg2—O3xv86.12 (5)O3xxvii—C4—Ba1xix62.77 (4)
O3xiv—Mg2—O3xv93.88 (5)O3xxviii—C4—Ba1xix149.14 (11)
O3xiii—Mg2—O3xvi93.88 (5)O3xxix—C4—Ba1xix62.77 (4)
O3xiv—Mg2—O3xvi86.12 (5)Ba1xvi—C4—Ba1xix99.00 (3)
O3xv—Mg2—O3xvi180.00 (7)O3xxvii—C4—Ba1xxii149.14 (11)
O3xiii—Mg2—O3xvii86.12 (5)O3xxviii—C4—Ba1xxii62.77 (4)
O3xiv—Mg2—O3xvii93.88 (5)O3xxix—C4—Ba1xxii62.77 (4)
O3xv—Mg2—O3xvii86.12 (5)Ba1xvi—C4—Ba1xxii99.00 (3)
O3xvi—Mg2—O3xvii93.88 (5)Ba1xix—C4—Ba1xxii99.00 (3)
O3xiii—Mg2—O3xviii93.88 (5)
Symmetry codes: (i) xy2/3, x4/3, z+2/3; (ii) x+y+2/3, x+4/3, z+1/3; (iii) x+1/3, y+2/3, z+2/3; (iv) x1/3, y2/3, z+1/3; (v) y2/3, x+y1/3, z+2/3; (vi) y+2/3, xy+1/3, z+1/3; (vii) xy+1/3, x1/3, z+2/3; (viii) x+y1/3, x+1/3, z+1/3; (ix) x4/3, y2/3, z+1/3; (x) y2/3, x+y+2/3, z+2/3; (xi) x+4/3, y+2/3, z+2/3; (xii) y+2/3, xy2/3, z+1/3; (xiii) y1/3, x+y+1/3, z+1/3; (xiv) y+1/3, xy1/3, z1/3; (xv) x+2/3, y+1/3, z+1/3; (xvi) x2/3, y1/3, z1/3; (xvii) xy1/3, x2/3, z+1/3; (xviii) x+y+1/3, x+2/3, z1/3; (xix) x+1/3, y+2/3, z1/3; (xx) x1/3, y2/3, z2/3; (xxi) x+2/3, y+1/3, z2/3; (xxii) x+1/3, y1/3, z1/3; (xxiii) x1/3, y+1/3, z2/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z1/3; (xxvii) x+y, x+1, z; (xxviii) x1, y1, z; (xxix) y+1, xy, z.
(norse_390) top
Crystal data top
C6Ba3Mg3O18Dx = 3.829 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3mCell parameters from 5088 reflections
a = 5.0206 (2) Åθ = 1.5–45°
c = 16.7875 (6) ŵ = 8.21 mm1
V = 366.46 (3) Å3T = 390 K
Z = 1Prismatic
F(000) = 3840.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.028
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.6°, θmin = 3.6°
Tmin = 0.7, Tmax = 0.8h = 910
5088 measured reflectionsk = 109
428 independent reflectionsl = 3317
428 reflections with I > 2σ(I)
Refinement top
Refinement on F214 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.014 w = 1/[σ2(Fo2) + (0.0092P)2 + 0.9072P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.030(Δ/σ)max < 0.001
S = 1.14Δρmax = 1.12 e Å3
428 reflectionsΔρmin = 0.61 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.50000.01363 (4)
Mg20.00000.00000.00000.01081 (14)
O30.85369 (12)0.7074 (2)0.25776 (7)0.0272 (2)
C40.00000.00000.26060 (10)0.0112 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.01199 (5)0.01199 (5)0.01689 (7)0.00600 (2)0.0000.000
Mg20.0093 (2)0.0093 (2)0.0138 (3)0.00466 (10)0.0000.000
O30.0361 (5)0.0102 (3)0.0267 (4)0.00512 (16)0.00206 (16)0.0041 (3)
C40.0108 (3)0.0108 (3)0.0119 (5)0.00541 (17)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.9447 (6)Mg2—O3xviii2.0627 (11)
Ba1—O3ii2.9447 (6)Mg2—Ba1xix4.0287 (1)
Ba1—O3iii2.9447 (6)Mg2—Ba1xx4.0287 (1)
Ba1—O3iv2.9447 (6)Mg2—Ba1xvi4.0287 (1)
Ba1—O3v2.9448 (6)Mg2—Ba1xxi4.0287 (1)
Ba1—O3vi2.9448 (6)Mg2—Ba1xxii4.0287 (1)
Ba1—O3vii2.9447 (6)Mg2—Ba1xxiii4.0287 (1)
Ba1—O3viii2.9447 (6)O3—C4xxiv1.2732 (11)
Ba1—O3ix2.9448 (6)O3—Mg2xxv2.0627 (11)
Ba1—O3x2.9448 (6)O3—Ba1xix2.9447 (6)
Ba1—O3xi2.9448 (6)O3—Ba1xxvi2.9448 (6)
Ba1—O3xii2.9448 (6)C4—O3xxvii1.2732 (11)
Mg2—O3xiii2.0627 (11)C4—O3xxviii1.2732 (11)
Mg2—O3xiv2.0627 (11)C4—O3xxix1.2732 (11)
Mg2—O3xv2.0627 (11)C4—Ba1xvi3.2998 (8)
Mg2—O3xvi2.0627 (11)C4—Ba1xix3.2998 (8)
Mg2—O3xvii2.0627 (11)C4—Ba1xxii3.2998 (8)
O3i—Ba1—O3ii180.00 (4)O3xiv—Mg2—O3xviii86.13 (5)
O3i—Ba1—O3iii57.15 (4)O3xv—Mg2—O3xviii93.87 (5)
O3ii—Ba1—O3iii122.85 (4)O3xvi—Mg2—O3xviii86.13 (5)
O3i—Ba1—O3iv122.85 (4)O3xvii—Mg2—O3xviii180.00 (5)
O3ii—Ba1—O3iv57.15 (4)O3xiii—Mg2—Ba1xix44.697 (16)
O3iii—Ba1—O3iv180.0O3xiv—Mg2—Ba1xix135.303 (16)
O3i—Ba1—O3v43.95 (4)O3xv—Mg2—Ba1xix98.05 (3)
O3ii—Ba1—O3v136.05 (4)O3xvi—Mg2—Ba1xix81.95 (3)
O3iii—Ba1—O3v95.48 (3)O3xvii—Mg2—Ba1xix44.699 (15)
O3iv—Ba1—O3v84.52 (3)O3xviii—Mg2—Ba1xix135.301 (15)
O3i—Ba1—O3vi136.05 (4)O3xiii—Mg2—Ba1xx135.303 (16)
O3ii—Ba1—O3vi43.95 (4)O3xiv—Mg2—Ba1xx44.697 (16)
O3iii—Ba1—O3vi84.52 (3)O3xv—Mg2—Ba1xx81.95 (3)
O3iv—Ba1—O3vi95.48 (3)O3xvi—Mg2—Ba1xx98.05 (3)
O3v—Ba1—O3vi180.0O3xvii—Mg2—Ba1xx135.301 (15)
O3i—Ba1—O3vii95.48 (3)O3xviii—Mg2—Ba1xx44.699 (15)
O3ii—Ba1—O3vii84.52 (3)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii43.95 (4)O3xiii—Mg2—Ba1xvi98.05 (3)
O3iv—Ba1—O3vii136.05 (4)O3xiv—Mg2—Ba1xvi81.95 (3)
O3v—Ba1—O3vii116.96 (4)O3xv—Mg2—Ba1xvi44.697 (16)
O3vi—Ba1—O3vii63.04 (4)O3xvi—Mg2—Ba1xvi135.303 (16)
O3i—Ba1—O3viii84.52 (3)O3xvii—Mg2—Ba1xvi44.699 (16)
O3ii—Ba1—O3viii95.48 (3)O3xviii—Mg2—Ba1xvi135.301 (16)
O3iii—Ba1—O3viii136.05 (4)Ba1xix—Mg2—Ba1xvi77.087 (2)
O3iv—Ba1—O3viii43.95 (4)Ba1xx—Mg2—Ba1xvi102.913 (2)
O3v—Ba1—O3viii63.04 (4)O3xiii—Mg2—Ba1xxi81.95 (3)
O3vi—Ba1—O3viii116.96 (4)O3xiv—Mg2—Ba1xxi98.05 (3)
O3vii—Ba1—O3viii180.0O3xv—Mg2—Ba1xxi135.303 (16)
O3i—Ba1—O3ix95.48 (3)O3xvi—Mg2—Ba1xxi44.697 (16)
O3ii—Ba1—O3ix84.52 (3)O3xvii—Mg2—Ba1xxi135.301 (16)
O3iii—Ba1—O3ix116.96 (4)O3xviii—Mg2—Ba1xxi44.699 (16)
O3iv—Ba1—O3ix63.04 (4)Ba1xix—Mg2—Ba1xxi102.913 (2)
O3v—Ba1—O3ix57.15 (4)Ba1xx—Mg2—Ba1xxi77.087 (2)
O3vi—Ba1—O3ix122.85 (4)Ba1xvi—Mg2—Ba1xxi180.0
O3vii—Ba1—O3ix95.48 (3)O3xiii—Mg2—Ba1xxii44.699 (15)
O3viii—Ba1—O3ix84.52 (3)O3xiv—Mg2—Ba1xxii135.301 (15)
O3i—Ba1—O3x84.52 (3)O3xv—Mg2—Ba1xxii44.699 (15)
O3ii—Ba1—O3x95.48 (3)O3xvi—Mg2—Ba1xxii135.301 (15)
O3iii—Ba1—O3x63.04 (4)O3xvii—Mg2—Ba1xxii98.06 (3)
O3iv—Ba1—O3x116.96 (4)O3xviii—Mg2—Ba1xxii81.94 (3)
O3v—Ba1—O3x122.85 (4)Ba1xix—Mg2—Ba1xxii77.087 (2)
O3vi—Ba1—O3x57.15 (4)Ba1xx—Mg2—Ba1xxii102.913 (2)
O3vii—Ba1—O3x84.52 (3)Ba1xvi—Mg2—Ba1xxii77.087 (2)
O3viii—Ba1—O3x95.48 (3)Ba1xxi—Mg2—Ba1xxii102.913 (2)
O3ix—Ba1—O3x180.00 (4)O3xiii—Mg2—Ba1xxiii135.301 (15)
O3i—Ba1—O3xi63.04 (4)O3xiv—Mg2—Ba1xxiii44.699 (15)
O3ii—Ba1—O3xi116.96 (4)O3xv—Mg2—Ba1xxiii135.301 (15)
O3iii—Ba1—O3xi84.52 (3)O3xvi—Mg2—Ba1xxiii44.699 (15)
O3iv—Ba1—O3xi95.48 (3)O3xvii—Mg2—Ba1xxiii81.94 (3)
O3v—Ba1—O3xi84.52 (3)O3xviii—Mg2—Ba1xxiii98.06 (3)
O3vi—Ba1—O3xi95.48 (3)Ba1xix—Mg2—Ba1xxiii102.913 (2)
O3vii—Ba1—O3xi122.85 (4)Ba1xx—Mg2—Ba1xxiii77.087 (2)
O3viii—Ba1—O3xi57.15 (4)Ba1xvi—Mg2—Ba1xxiii102.913 (2)
O3ix—Ba1—O3xi136.05 (4)Ba1xxi—Mg2—Ba1xxiii77.087 (2)
O3x—Ba1—O3xi43.95 (4)Ba1xxii—Mg2—Ba1xxiii180.0
O3i—Ba1—O3xii116.96 (4)C4xxiv—O3—Mg2xxv139.90 (11)
O3ii—Ba1—O3xii63.04 (4)C4xxiv—O3—Ba1xix94.56 (5)
O3iii—Ba1—O3xii95.48 (3)Mg2xxv—O3—Ba1xix105.78 (3)
O3iv—Ba1—O3xii84.52 (3)C4xxiv—O3—Ba1xxvi94.56 (5)
O3v—Ba1—O3xii95.48 (3)Mg2xxv—O3—Ba1xxvi105.78 (3)
O3vi—Ba1—O3xii84.52 (3)Ba1xix—O3—Ba1xxvi116.96 (4)
O3vii—Ba1—O3xii57.15 (4)O3xxvii—C4—O3xxviii119.861 (13)
O3viii—Ba1—O3xii122.85 (4)O3xxvii—C4—O3xxix119.861 (13)
O3ix—Ba1—O3xii43.95 (4)O3xxviii—C4—O3xxix119.861 (13)
O3x—Ba1—O3xii136.05 (4)O3xxvii—C4—Ba1xvi62.82 (4)
O3xi—Ba1—O3xii180.0O3xxviii—C4—Ba1xvi149.31 (12)
O3xiii—Mg2—O3xiv180.00 (5)O3xxix—C4—Ba1xvi62.82 (4)
O3xiii—Mg2—O3xv86.13 (5)O3xxvii—C4—Ba1xix149.31 (12)
O3xiv—Mg2—O3xv93.87 (5)O3xxviii—C4—Ba1xix62.82 (4)
O3xiii—Mg2—O3xvi93.87 (5)O3xxix—C4—Ba1xix62.82 (4)
O3xiv—Mg2—O3xvi86.13 (5)Ba1xvi—C4—Ba1xix99.06 (3)
O3xv—Mg2—O3xvi180.00 (7)O3xxvii—C4—Ba1xxii62.82 (4)
O3xiii—Mg2—O3xvii86.13 (5)O3xxviii—C4—Ba1xxii62.82 (4)
O3xiv—Mg2—O3xvii93.87 (5)O3xxix—C4—Ba1xxii149.31 (12)
O3xv—Mg2—O3xvii86.13 (5)Ba1xvi—C4—Ba1xxii99.06 (3)
O3xvi—Mg2—O3xvii93.87 (5)Ba1xix—C4—Ba1xxii99.06 (3)
O3xiii—Mg2—O3xviii93.87 (5)
Symmetry codes: (i) x+1/3, y+2/3, z+2/3; (ii) x1/3, y2/3, z+1/3; (iii) y2/3, x+y+2/3, z+2/3; (iv) y+2/3, xy2/3, z+1/3; (v) xy2/3, x4/3, z+2/3; (vi) x+y+2/3, x+4/3, z+1/3; (vii) xy+1/3, x1/3, z+2/3; (viii) x+y1/3, x+1/3, z+1/3; (ix) y2/3, x+y1/3, z+2/3; (x) y+2/3, xy+1/3, z+1/3; (xi) x4/3, y2/3, z+1/3; (xii) x+4/3, y+2/3, z+2/3; (xiii) y1/3, x+y+1/3, z+1/3; (xiv) y+1/3, xy1/3, z1/3; (xv) x+2/3, y+1/3, z+1/3; (xvi) x2/3, y1/3, z1/3; (xvii) xy1/3, x2/3, z+1/3; (xviii) x+y+1/3, x+2/3, z1/3; (xix) x+1/3, y+2/3, z1/3; (xx) x1/3, y2/3, z2/3; (xxi) x+2/3, y+1/3, z2/3; (xxii) x+1/3, y1/3, z1/3; (xxiii) x1/3, y+1/3, z2/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z1/3; (xxvii) x1, y1, z; (xxviii) y+1, xy, z; (xxix) x+y, x+1, z.
(norse_400) top
Crystal data top
C6Ba3Mg3O18Dx = 3.824 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3mCell parameters from 5074 reflections
a = 5.0217 (2) Åθ = 1.5–45°
c = 16.8037 (6) ŵ = 8.20 mm1
V = 366.98 (3) Å3T = 399 K
Z = 1Prismatic
F(000) = 3840.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.029
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.5°, θmin = 3.6°
Tmin = 0.7, Tmax = 0.8h = 910
5074 measured reflectionsk = 109
429 independent reflectionsl = 3317
429 reflections with I > 2σ(I)
Refinement top
Refinement on F214 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.014 w = 1/[σ2(Fo2) + (0.0116P)2 + 0.924P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.032(Δ/σ)max < 0.001
S = 1.12Δρmax = 1.27 e Å3
429 reflectionsΔρmin = 0.68 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.50000.01395 (4)
Mg20.00000.00000.00000.01121 (15)
O30.85358 (13)0.7072 (3)0.25775 (7)0.0277 (2)
C40.00000.00000.26075 (11)0.0113 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.01227 (5)0.01227 (5)0.01733 (7)0.00613 (2)0.0000.000
Mg20.0096 (2)0.0096 (2)0.0145 (4)0.00479 (11)0.0000.000
O30.0367 (5)0.0104 (3)0.0271 (4)0.00521 (17)0.00210 (16)0.0042 (3)
C40.0109 (3)0.0109 (3)0.0123 (5)0.00543 (17)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.9458 (7)Mg2—O3xviii2.0631 (11)
Ba1—O3ii2.9458 (7)Mg2—Ba1xix4.0310 (1)
Ba1—O3iii2.9458 (7)Mg2—Ba1xx4.0310 (1)
Ba1—O3iv2.9458 (7)Mg2—Ba1xxi4.0310 (1)
Ba1—O3v2.9458 (7)Mg2—Ba1xviii4.0310 (1)
Ba1—O3vi2.9458 (7)Mg2—Ba1xxii4.0310 (1)
Ba1—O3vii2.9458 (7)Mg2—Ba1xxiii4.0310 (1)
Ba1—O3viii2.9458 (7)O3—C4xxiv1.2745 (11)
Ba1—O3ix2.9458 (7)O3—Mg2xxv2.0631 (11)
Ba1—O3x2.9458 (7)O3—Ba1xx2.9458 (7)
Ba1—O3xi2.9458 (7)O3—Ba1xxvi2.9458 (7)
Ba1—O3xii2.9458 (7)C4—O3xxvii1.2745 (11)
Mg2—O3xiii2.0631 (11)C4—O3xxviii1.2745 (11)
Mg2—O3xiv2.0631 (11)C4—O3xxix1.2746 (11)
Mg2—O3xv2.0631 (11)C4—Ba1xviii3.3023 (9)
Mg2—O3xvi2.0631 (11)C4—Ba1xx3.3023 (9)
Mg2—O3xvii2.0631 (11)C4—Ba1xxiii3.3023 (9)
O3i—Ba1—O3ii180.0O3xiv—Mg2—O3xviii86.07 (5)
O3i—Ba1—O3iii57.10 (4)O3xv—Mg2—O3xviii93.93 (5)
O3ii—Ba1—O3iii122.90 (4)O3xvi—Mg2—O3xviii86.07 (5)
O3i—Ba1—O3iv122.90 (4)O3xvii—Mg2—O3xviii180.00 (6)
O3ii—Ba1—O3iv57.10 (4)O3xiii—Mg2—Ba1xix135.327 (16)
O3iii—Ba1—O3iv180.0O3xiv—Mg2—Ba1xix44.673 (16)
O3i—Ba1—O3v43.98 (4)O3xv—Mg2—Ba1xix135.327 (16)
O3ii—Ba1—O3v136.02 (4)O3xvi—Mg2—Ba1xix44.673 (16)
O3iii—Ba1—O3v95.46 (3)O3xvii—Mg2—Ba1xix82.01 (4)
O3iv—Ba1—O3v84.54 (3)O3xviii—Mg2—Ba1xix97.99 (4)
O3i—Ba1—O3vi136.02 (4)O3xiii—Mg2—Ba1xx44.673 (16)
O3ii—Ba1—O3vi43.98 (4)O3xiv—Mg2—Ba1xx135.327 (16)
O3iii—Ba1—O3vi84.54 (3)O3xv—Mg2—Ba1xx44.673 (16)
O3iv—Ba1—O3vi95.46 (3)O3xvi—Mg2—Ba1xx135.327 (16)
O3v—Ba1—O3vi180.0O3xvii—Mg2—Ba1xx97.99 (4)
O3i—Ba1—O3vii95.46 (3)O3xviii—Mg2—Ba1xx82.01 (4)
O3ii—Ba1—O3vii84.54 (3)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii43.98 (4)O3xiii—Mg2—Ba1xxi82.01 (4)
O3iv—Ba1—O3vii136.02 (4)O3xiv—Mg2—Ba1xxi97.99 (4)
O3v—Ba1—O3vii116.94 (4)O3xv—Mg2—Ba1xxi135.327 (16)
O3vi—Ba1—O3vii63.06 (4)O3xvi—Mg2—Ba1xxi44.673 (16)
O3i—Ba1—O3viii84.54 (3)O3xvii—Mg2—Ba1xxi135.327 (16)
O3ii—Ba1—O3viii95.46 (3)O3xviii—Mg2—Ba1xxi44.673 (16)
O3iii—Ba1—O3viii136.02 (4)Ba1xix—Mg2—Ba1xxi77.054 (2)
O3iv—Ba1—O3viii43.98 (4)Ba1xx—Mg2—Ba1xxi102.946 (2)
O3v—Ba1—O3viii63.06 (4)O3xiii—Mg2—Ba1xviii97.99 (4)
O3vi—Ba1—O3viii116.94 (4)O3xiv—Mg2—Ba1xviii82.01 (4)
O3vii—Ba1—O3viii180.0O3xv—Mg2—Ba1xviii44.673 (16)
O3i—Ba1—O3ix95.46 (3)O3xvi—Mg2—Ba1xviii135.327 (16)
O3ii—Ba1—O3ix84.54 (3)O3xvii—Mg2—Ba1xviii44.673 (16)
O3iii—Ba1—O3ix116.94 (4)O3xviii—Mg2—Ba1xviii135.327 (16)
O3iv—Ba1—O3ix63.06 (4)Ba1xix—Mg2—Ba1xviii102.946 (2)
O3v—Ba1—O3ix57.10 (4)Ba1xx—Mg2—Ba1xviii77.054 (2)
O3vi—Ba1—O3ix122.90 (4)Ba1xxi—Mg2—Ba1xviii180.0
O3vii—Ba1—O3ix95.46 (3)O3xiii—Mg2—Ba1xxii135.327 (16)
O3viii—Ba1—O3ix84.54 (3)O3xiv—Mg2—Ba1xxii44.673 (16)
O3i—Ba1—O3x84.54 (3)O3xv—Mg2—Ba1xxii82.01 (3)
O3ii—Ba1—O3x95.46 (3)O3xvi—Mg2—Ba1xxii97.99 (3)
O3iii—Ba1—O3x63.06 (4)O3xvii—Mg2—Ba1xxii135.327 (16)
O3iv—Ba1—O3x116.94 (4)O3xviii—Mg2—Ba1xxii44.673 (16)
O3v—Ba1—O3x122.90 (4)Ba1xix—Mg2—Ba1xxii77.054 (2)
O3vi—Ba1—O3x57.10 (4)Ba1xx—Mg2—Ba1xxii102.946 (2)
O3vii—Ba1—O3x84.54 (3)Ba1xxi—Mg2—Ba1xxii77.054 (2)
O3viii—Ba1—O3x95.46 (3)Ba1xviii—Mg2—Ba1xxii102.946 (2)
O3ix—Ba1—O3x180.00 (4)O3xiii—Mg2—Ba1xxiii44.673 (16)
O3i—Ba1—O3xi63.06 (4)O3xiv—Mg2—Ba1xxiii135.327 (16)
O3ii—Ba1—O3xi116.94 (4)O3xv—Mg2—Ba1xxiii97.99 (3)
O3iii—Ba1—O3xi84.54 (3)O3xvi—Mg2—Ba1xxiii82.01 (3)
O3iv—Ba1—O3xi95.46 (3)O3xvii—Mg2—Ba1xxiii44.673 (16)
O3v—Ba1—O3xi84.54 (3)O3xviii—Mg2—Ba1xxiii135.327 (16)
O3vi—Ba1—O3xi95.46 (3)Ba1xix—Mg2—Ba1xxiii102.946 (2)
O3vii—Ba1—O3xi122.90 (4)Ba1xx—Mg2—Ba1xxiii77.054 (2)
O3viii—Ba1—O3xi57.10 (4)Ba1xxi—Mg2—Ba1xxiii102.946 (2)
O3ix—Ba1—O3xi136.03 (4)Ba1xviii—Mg2—Ba1xxiii77.054 (2)
O3x—Ba1—O3xi43.97 (4)Ba1xxii—Mg2—Ba1xxiii180.0
O3i—Ba1—O3xii116.94 (4)C4xxiv—O3—Mg2xxv139.73 (12)
O3ii—Ba1—O3xii63.06 (4)C4xxiv—O3—Ba1xx94.61 (5)
O3iii—Ba1—O3xii95.46 (3)Mg2xxv—O3—Ba1xx105.83 (3)
O3iv—Ba1—O3xii84.54 (3)C4xxiv—O3—Ba1xxvi94.61 (5)
O3v—Ba1—O3xii95.46 (3)Mg2xxv—O3—Ba1xxvi105.83 (3)
O3vi—Ba1—O3xii84.54 (3)Ba1xx—O3—Ba1xxvi116.94 (4)
O3vii—Ba1—O3xii57.10 (4)O3xxvii—C4—O3xxviii119.846 (14)
O3viii—Ba1—O3xii122.90 (4)O3xxvii—C4—O3xxix119.844 (14)
O3ix—Ba1—O3xii43.97 (4)O3xxviii—C4—O3xxix119.844 (14)
O3x—Ba1—O3xii136.03 (5)O3xxvii—C4—Ba1xviii62.77 (5)
O3xi—Ba1—O3xii180.0O3xxviii—C4—Ba1xviii149.13 (12)
O3xiii—Mg2—O3xiv180.00 (5)O3xxix—C4—Ba1xviii62.77 (5)
O3xiii—Mg2—O3xv86.07 (5)O3xxvii—C4—Ba1xx149.13 (12)
O3xiv—Mg2—O3xv93.93 (5)O3xxviii—C4—Ba1xx62.77 (5)
O3xiii—Mg2—O3xvi93.93 (5)O3xxix—C4—Ba1xx62.77 (5)
O3xiv—Mg2—O3xvi86.07 (5)Ba1xviii—C4—Ba1xx98.99 (3)
O3xv—Mg2—O3xvi180.00 (6)O3xxvii—C4—Ba1xxiii62.77 (5)
O3xiii—Mg2—O3xvii86.07 (5)O3xxviii—C4—Ba1xxiii62.77 (5)
O3xiv—Mg2—O3xvii93.93 (5)O3xxix—C4—Ba1xxiii149.13 (12)
O3xv—Mg2—O3xvii86.07 (5)Ba1xviii—C4—Ba1xxiii98.99 (3)
O3xvi—Mg2—O3xvii93.93 (5)Ba1xx—C4—Ba1xxiii98.99 (3)
O3xiii—Mg2—O3xviii93.93 (5)
Symmetry codes: (i) x+1/3, y+2/3, z+2/3; (ii) x1/3, y2/3, z+1/3; (iii) y2/3, x+y+2/3, z+2/3; (iv) y+2/3, xy2/3, z+1/3; (v) xy2/3, x4/3, z+2/3; (vi) x+y+2/3, x+4/3, z+1/3; (vii) xy+1/3, x1/3, z+2/3; (viii) x+y1/3, x+1/3, z+1/3; (ix) y2/3, x+y1/3, z+2/3; (x) y+2/3, xy+1/3, z+1/3; (xi) x4/3, y2/3, z+1/3; (xii) x+4/3, y+2/3, z+2/3; (xiii) y1/3, x+y+1/3, z+1/3; (xiv) y+1/3, xy1/3, z1/3; (xv) xy1/3, x2/3, z+1/3; (xvi) x+y+1/3, x+2/3, z1/3; (xvii) x+2/3, y+1/3, z+1/3; (xviii) x2/3, y1/3, z1/3; (xix) x1/3, y2/3, z2/3; (xx) x+1/3, y+2/3, z1/3; (xxi) x+2/3, y+1/3, z2/3; (xxii) x1/3, y+1/3, z2/3; (xxiii) x+1/3, y1/3, z1/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z1/3; (xxvii) x1, y1, z; (xxviii) y+1, xy, z; (xxix) x+y, x+1, z.
(norse_420) top
Crystal data top
C6Ba3Mg3O18Dx = 3.818 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3mCell parameters from 5148 reflections
a = 5.0224 (2) Åθ = 1.5–45°
c = 16.8222 (8) ŵ = 8.19 mm1
V = 367.48 (3) Å3T = 420 K
Z = 1Prismatic
F(000) = 3840.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.029
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.5°, θmin = 3.6°
Tmin = 0.7, Tmax = 0.8h = 910
5148 measured reflectionsk = 109
428 independent reflectionsl = 3317
428 reflections with I > 2σ(I)
Refinement top
Refinement on F214 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.013 w = 1/[σ2(Fo2) + (0.0095P)2 + 0.744P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.031(Δ/σ)max < 0.001
S = 1.18Δρmax = 1.05 e Å3
428 reflectionsΔρmin = 0.72 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.50000.01455 (4)
Mg20.00000.00000.00000.01152 (14)
O30.85374 (12)0.7075 (2)0.25774 (7)0.0283 (2)
C40.00000.00000.26077 (10)0.0119 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.01277 (5)0.01277 (5)0.01812 (7)0.00638 (2)0.0000.000
Mg20.0098 (2)0.0098 (2)0.0149 (4)0.00492 (10)0.0000.000
O30.0370 (5)0.0110 (3)0.0284 (4)0.00550 (16)0.00219 (16)0.0044 (3)
C40.0116 (3)0.0116 (3)0.0126 (5)0.00580 (17)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.9470 (6)Mg2—O3xviii2.0653 (11)
Ba1—O3ii2.9470 (6)Mg2—Ba1xix4.0334 (1)
Ba1—O3iii2.9470 (6)Mg2—Ba1xx4.0334 (1)
Ba1—O3iv2.9470 (6)Mg2—Ba1xvi4.0334 (1)
Ba1—O3v2.9471 (6)Mg2—Ba1xxi4.0334 (1)
Ba1—O3vi2.9471 (6)Mg2—Ba1xxii4.0335 (1)
Ba1—O3vii2.9471 (6)Mg2—Ba1xxiii4.0335 (1)
Ba1—O3viii2.9471 (6)O3—C4xxiv1.2733 (11)
Ba1—O3ix2.9471 (6)O3—Mg2xxv2.0653 (11)
Ba1—O3x2.9471 (6)O3—Ba1xix2.9470 (6)
Ba1—O3xi2.9471 (6)O3—Ba1xxvi2.9471 (6)
Ba1—O3xii2.9471 (6)C4—O3xxvii1.2733 (11)
Mg2—O3xiii2.0653 (11)C4—O3xxviii1.2733 (11)
Mg2—O3xiv2.0653 (11)C4—O3xxix1.2733 (11)
Mg2—O3xv2.0653 (11)C4—Ba1xvi3.3037 (8)
Mg2—O3xvi2.0653 (11)C4—Ba1xix3.3037 (8)
Mg2—O3xvii2.0653 (11)C4—Ba1xxii3.3037 (8)
O3i—Ba1—O3ii180.00 (4)O3xiv—Mg2—O3xviii86.06 (5)
O3i—Ba1—O3iii57.14 (4)O3xv—Mg2—O3xviii93.94 (5)
O3ii—Ba1—O3iii122.86 (4)O3xvi—Mg2—O3xviii86.06 (5)
O3i—Ba1—O3iv122.86 (4)O3xvii—Mg2—O3xviii180.00 (6)
O3ii—Ba1—O3iv57.14 (4)O3xiii—Mg2—Ba1xix44.665 (16)
O3iii—Ba1—O3iv180.0O3xiv—Mg2—Ba1xix135.335 (16)
O3i—Ba1—O3v43.91 (4)O3xv—Mg2—Ba1xix97.96 (3)
O3ii—Ba1—O3v136.09 (4)O3xvi—Mg2—Ba1xix82.04 (3)
O3iii—Ba1—O3v95.43 (3)O3xvii—Mg2—Ba1xix44.666 (16)
O3iv—Ba1—O3v84.57 (3)O3xviii—Mg2—Ba1xix135.334 (16)
O3i—Ba1—O3vi136.09 (4)O3xiii—Mg2—Ba1xx135.335 (16)
O3ii—Ba1—O3vi43.91 (4)O3xiv—Mg2—Ba1xx44.665 (16)
O3iii—Ba1—O3vi84.57 (3)O3xv—Mg2—Ba1xx82.04 (3)
O3iv—Ba1—O3vi95.43 (3)O3xvi—Mg2—Ba1xx97.96 (3)
O3v—Ba1—O3vi180.0O3xvii—Mg2—Ba1xx135.334 (16)
O3i—Ba1—O3vii95.43 (3)O3xviii—Mg2—Ba1xx44.666 (16)
O3ii—Ba1—O3vii84.57 (3)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii43.91 (4)O3xiii—Mg2—Ba1xvi97.96 (3)
O3iv—Ba1—O3vii136.09 (4)O3xiv—Mg2—Ba1xvi82.04 (3)
O3v—Ba1—O3vii116.88 (4)O3xv—Mg2—Ba1xvi44.665 (16)
O3vi—Ba1—O3vii63.12 (4)O3xvi—Mg2—Ba1xvi135.335 (16)
O3i—Ba1—O3viii84.57 (3)O3xvii—Mg2—Ba1xvi44.666 (16)
O3ii—Ba1—O3viii95.43 (3)O3xviii—Mg2—Ba1xvi135.334 (16)
O3iii—Ba1—O3viii136.09 (4)Ba1xix—Mg2—Ba1xvi77.012 (3)
O3iv—Ba1—O3viii43.91 (4)Ba1xx—Mg2—Ba1xvi102.988 (3)
O3v—Ba1—O3viii63.12 (4)O3xiii—Mg2—Ba1xxi82.04 (3)
O3vi—Ba1—O3viii116.88 (4)O3xiv—Mg2—Ba1xxi97.96 (3)
O3vii—Ba1—O3viii180.0O3xv—Mg2—Ba1xxi135.335 (16)
O3i—Ba1—O3ix95.43 (3)O3xvi—Mg2—Ba1xxi44.665 (16)
O3ii—Ba1—O3ix84.57 (3)O3xvii—Mg2—Ba1xxi135.334 (16)
O3iii—Ba1—O3ix116.88 (4)O3xviii—Mg2—Ba1xxi44.666 (16)
O3iv—Ba1—O3ix63.12 (4)Ba1xix—Mg2—Ba1xxi102.988 (3)
O3v—Ba1—O3ix57.14 (4)Ba1xx—Mg2—Ba1xxi77.012 (3)
O3vi—Ba1—O3ix122.86 (4)Ba1xvi—Mg2—Ba1xxi180.0
O3vii—Ba1—O3ix95.43 (3)O3xiii—Mg2—Ba1xxii44.666 (16)
O3viii—Ba1—O3ix84.57 (3)O3xiv—Mg2—Ba1xxii135.334 (16)
O3i—Ba1—O3x84.57 (3)O3xv—Mg2—Ba1xxii44.666 (16)
O3ii—Ba1—O3x95.43 (3)O3xvi—Mg2—Ba1xxii135.334 (16)
O3iii—Ba1—O3x63.12 (4)O3xvii—Mg2—Ba1xxii97.96 (3)
O3iv—Ba1—O3x116.88 (4)O3xviii—Mg2—Ba1xxii82.04 (3)
O3v—Ba1—O3x122.86 (4)Ba1xix—Mg2—Ba1xxii77.012 (2)
O3vi—Ba1—O3x57.14 (4)Ba1xx—Mg2—Ba1xxii102.988 (2)
O3vii—Ba1—O3x84.57 (3)Ba1xvi—Mg2—Ba1xxii77.012 (3)
O3viii—Ba1—O3x95.43 (3)Ba1xxi—Mg2—Ba1xxii102.988 (3)
O3ix—Ba1—O3x180.00 (4)O3xiii—Mg2—Ba1xxiii135.334 (16)
O3i—Ba1—O3xi63.12 (4)O3xiv—Mg2—Ba1xxiii44.666 (16)
O3ii—Ba1—O3xi116.88 (4)O3xv—Mg2—Ba1xxiii135.334 (16)
O3iii—Ba1—O3xi84.57 (3)O3xvi—Mg2—Ba1xxiii44.666 (16)
O3iv—Ba1—O3xi95.43 (3)O3xvii—Mg2—Ba1xxiii82.04 (3)
O3v—Ba1—O3xi84.57 (3)O3xviii—Mg2—Ba1xxiii97.96 (3)
O3vi—Ba1—O3xi95.43 (3)Ba1xix—Mg2—Ba1xxiii102.988 (2)
O3vii—Ba1—O3xi122.86 (4)Ba1xx—Mg2—Ba1xxiii77.012 (2)
O3viii—Ba1—O3xi57.14 (4)Ba1xvi—Mg2—Ba1xxiii102.988 (3)
O3ix—Ba1—O3xi136.09 (4)Ba1xxi—Mg2—Ba1xxiii77.012 (3)
O3x—Ba1—O3xi43.91 (4)Ba1xxii—Mg2—Ba1xxiii180.0
O3i—Ba1—O3xii116.88 (4)C4xxiv—O3—Mg2xxv139.70 (11)
O3ii—Ba1—O3xii63.12 (4)C4xxiv—O3—Ba1xix94.65 (5)
O3iii—Ba1—O3xii95.43 (3)Mg2xxv—O3—Ba1xix105.82 (3)
O3iv—Ba1—O3xii84.57 (3)C4xxiv—O3—Ba1xxvi94.65 (5)
O3v—Ba1—O3xii95.43 (3)Mg2xxv—O3—Ba1xxvi105.82 (3)
O3vi—Ba1—O3xii84.57 (3)Ba1xix—O3—Ba1xxvi116.88 (4)
O3vii—Ba1—O3xii57.14 (4)O3xxvii—C4—O3xxviii119.841 (14)
O3viii—Ba1—O3xii122.86 (4)O3xxvii—C4—O3xxix119.841 (14)
O3ix—Ba1—O3xii43.91 (4)O3xxviii—C4—O3xxix119.841 (14)
O3x—Ba1—O3xii136.09 (4)O3xxvii—C4—Ba1xvi62.76 (4)
O3xi—Ba1—O3xii180.0O3xxviii—C4—Ba1xvi149.07 (12)
O3xiii—Mg2—O3xiv180.00 (5)O3xxix—C4—Ba1xvi62.76 (4)
O3xiii—Mg2—O3xv86.06 (5)O3xxvii—C4—Ba1xix149.07 (12)
O3xiv—Mg2—O3xv93.94 (5)O3xxviii—C4—Ba1xix62.76 (4)
O3xiii—Mg2—O3xvi93.94 (5)O3xxix—C4—Ba1xix62.76 (4)
O3xiv—Mg2—O3xvi86.06 (5)Ba1xvi—C4—Ba1xix98.95 (3)
O3xv—Mg2—O3xvi180.00 (5)O3xxvii—C4—Ba1xxii62.76 (4)
O3xiii—Mg2—O3xvii86.06 (5)O3xxviii—C4—Ba1xxii62.76 (4)
O3xiv—Mg2—O3xvii93.94 (5)O3xxix—C4—Ba1xxii149.07 (12)
O3xv—Mg2—O3xvii86.06 (5)Ba1xvi—C4—Ba1xxii98.95 (3)
O3xvi—Mg2—O3xvii93.94 (5)Ba1xix—C4—Ba1xxii98.95 (3)
O3xiii—Mg2—O3xviii93.94 (5)
Symmetry codes: (i) x+1/3, y+2/3, z+2/3; (ii) x1/3, y2/3, z+1/3; (iii) y2/3, x+y+2/3, z+2/3; (iv) y+2/3, xy2/3, z+1/3; (v) xy2/3, x4/3, z+2/3; (vi) x+y+2/3, x+4/3, z+1/3; (vii) xy+1/3, x1/3, z+2/3; (viii) x+y1/3, x+1/3, z+1/3; (ix) y2/3, x+y1/3, z+2/3; (x) y+2/3, xy+1/3, z+1/3; (xi) x4/3, y2/3, z+1/3; (xii) x+4/3, y+2/3, z+2/3; (xiii) y1/3, x+y+1/3, z+1/3; (xiv) y+1/3, xy1/3, z1/3; (xv) x+2/3, y+1/3, z+1/3; (xvi) x2/3, y1/3, z1/3; (xvii) xy1/3, x2/3, z+1/3; (xviii) x+y+1/3, x+2/3, z1/3; (xix) x+1/3, y+2/3, z1/3; (xx) x1/3, y2/3, z2/3; (xxi) x+2/3, y+1/3, z2/3; (xxii) x+1/3, y1/3, z1/3; (xxiii) x1/3, y+1/3, z2/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z1/3; (xxvii) x1, y1, z; (xxviii) y+1, xy, z; (xxix) x+y, x+1, z.
(norse_440) top
Crystal data top
C6Ba3Mg3O18Dx = 3.809 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3mCell parameters from 4994 reflections
a = 5.0228 (7) Åθ = 1.5–45°
c = 16.862 (3) ŵ = 8.17 mm1
V = 368.41 (13) Å3T = 440 K
Z = 1Prismatic
F(000) = 3840.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.028
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.3°, θmin = 3.6°
Tmin = 0.7, Tmax = 0.8h = 910
4994 measured reflectionsk = 109
423 independent reflectionsl = 3217
423 reflections with I > 2σ(I)
Refinement top
Refinement on F214 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.014 w = 1/[σ2(Fo2) + (0.0114P)2 + 0.7897P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.032(Δ/σ)max < 0.001
S = 1.15Δρmax = 1.10 e Å3
423 reflectionsΔρmin = 0.69 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.50000.01522 (4)
Mg20.00000.00000.00000.01213 (15)
O30.85370 (13)0.7074 (3)0.25779 (8)0.0293 (2)
C40.00000.00000.26081 (11)0.0123 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.01340 (5)0.01340 (5)0.01886 (7)0.00670 (2)0.0000.000
Mg20.0104 (2)0.0104 (2)0.0157 (4)0.00518 (11)0.0000.000
O30.0380 (5)0.0115 (4)0.0296 (5)0.00573 (18)0.00234 (17)0.0047 (3)
C40.0121 (4)0.0121 (4)0.0129 (6)0.00603 (18)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.9495 (8)Mg2—O3xviii2.0665 (12)
Ba1—O3ii2.9495 (8)Mg2—Ba1xix4.0382 (5)
Ba1—O3iii2.9495 (8)Mg2—Ba1xx4.0382 (5)
Ba1—O3iv2.9495 (8)Mg2—Ba1xvi4.0382 (5)
Ba1—O3v2.9495 (8)Mg2—Ba1xxi4.0382 (5)
Ba1—O3vi2.9495 (8)Mg2—Ba1xxii4.0382 (5)
Ba1—O3vii2.9495 (8)Mg2—Ba1xxiii4.0382 (5)
Ba1—O3viii2.9495 (8)O3—C4xxiv1.2737 (12)
Ba1—O3ix2.9495 (8)O3—Mg2xxv2.0665 (12)
Ba1—O3x2.9495 (8)O3—Ba1xix2.9495 (8)
Ba1—O3xi2.9495 (8)O3—Ba1xxvi2.9495 (8)
Ba1—O3xii2.9495 (8)C4—O3xxvii1.2737 (12)
Mg2—O3xiii2.0665 (12)C4—O3xxviii1.2737 (12)
Mg2—O3xiv2.0665 (12)C4—O3xxix1.2737 (12)
Mg2—O3xv2.0665 (12)C4—Ba1xvi3.3060 (10)
Mg2—O3xvi2.0665 (12)C4—Ba1xix3.3060 (10)
Mg2—O3xvii2.0665 (12)C4—Ba1xxii3.3060 (10)
O3i—Ba1—O3ii180.0O3xiv—Mg2—O3xviii85.99 (5)
O3i—Ba1—O3iii57.08 (4)O3xv—Mg2—O3xviii94.01 (5)
O3ii—Ba1—O3iii122.92 (4)O3xvi—Mg2—O3xviii85.99 (5)
O3i—Ba1—O3iv122.92 (4)O3xvii—Mg2—O3xviii180.00 (6)
O3ii—Ba1—O3iv57.08 (4)O3xiii—Mg2—Ba1xix44.625 (18)
O3iii—Ba1—O3iv180.0O3xiv—Mg2—Ba1xix135.375 (18)
O3i—Ba1—O3v43.89 (5)O3xv—Mg2—Ba1xix97.84 (4)
O3ii—Ba1—O3v136.11 (5)O3xvi—Mg2—Ba1xix82.16 (4)
O3iii—Ba1—O3v95.33 (3)O3xvii—Mg2—Ba1xix44.626 (17)
O3iv—Ba1—O3v84.67 (3)O3xviii—Mg2—Ba1xix135.374 (17)
O3i—Ba1—O3vi136.11 (5)O3xiii—Mg2—Ba1xx135.375 (18)
O3ii—Ba1—O3vi43.89 (5)O3xiv—Mg2—Ba1xx44.625 (18)
O3iii—Ba1—O3vi84.67 (3)O3xv—Mg2—Ba1xx82.16 (4)
O3iv—Ba1—O3vi95.33 (3)O3xvi—Mg2—Ba1xx97.84 (4)
O3v—Ba1—O3vi180.0O3xvii—Mg2—Ba1xx135.374 (17)
O3i—Ba1—O3vii95.33 (3)O3xviii—Mg2—Ba1xx44.626 (17)
O3ii—Ba1—O3vii84.67 (3)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii43.89 (5)O3xiii—Mg2—Ba1xvi97.84 (4)
O3iv—Ba1—O3vii136.11 (5)O3xiv—Mg2—Ba1xvi82.16 (4)
O3v—Ba1—O3vii116.74 (4)O3xv—Mg2—Ba1xvi44.625 (18)
O3vi—Ba1—O3vii63.26 (4)O3xvi—Mg2—Ba1xvi135.375 (17)
O3i—Ba1—O3viii84.67 (3)O3xvii—Mg2—Ba1xvi44.626 (17)
O3ii—Ba1—O3viii95.33 (3)O3xviii—Mg2—Ba1xvi135.374 (17)
O3iii—Ba1—O3viii136.11 (5)Ba1xix—Mg2—Ba1xvi76.911 (11)
O3iv—Ba1—O3viii43.89 (5)Ba1xx—Mg2—Ba1xvi103.089 (11)
O3v—Ba1—O3viii63.26 (4)O3xiii—Mg2—Ba1xxi82.16 (4)
O3vi—Ba1—O3viii116.74 (4)O3xiv—Mg2—Ba1xxi97.84 (4)
O3vii—Ba1—O3viii180.0O3xv—Mg2—Ba1xxi135.375 (17)
O3i—Ba1—O3ix95.33 (3)O3xvi—Mg2—Ba1xxi44.625 (18)
O3ii—Ba1—O3ix84.67 (3)O3xvii—Mg2—Ba1xxi135.374 (17)
O3iii—Ba1—O3ix116.74 (4)O3xviii—Mg2—Ba1xxi44.626 (17)
O3iv—Ba1—O3ix63.26 (4)Ba1xix—Mg2—Ba1xxi103.089 (11)
O3v—Ba1—O3ix57.08 (4)Ba1xx—Mg2—Ba1xxi76.911 (11)
O3vi—Ba1—O3ix122.92 (4)Ba1xvi—Mg2—Ba1xxi180.0
O3vii—Ba1—O3ix95.33 (3)O3xiii—Mg2—Ba1xxii44.626 (17)
O3viii—Ba1—O3ix84.67 (3)O3xiv—Mg2—Ba1xxii135.374 (17)
O3i—Ba1—O3x84.67 (3)O3xv—Mg2—Ba1xxii44.626 (17)
O3ii—Ba1—O3x95.33 (3)O3xvi—Mg2—Ba1xxii135.374 (17)
O3iii—Ba1—O3x63.26 (4)O3xvii—Mg2—Ba1xxii97.84 (4)
O3iv—Ba1—O3x116.74 (4)O3xviii—Mg2—Ba1xxii82.16 (4)
O3v—Ba1—O3x122.92 (4)Ba1xix—Mg2—Ba1xxii76.911 (11)
O3vi—Ba1—O3x57.08 (4)Ba1xx—Mg2—Ba1xxii103.089 (11)
O3vii—Ba1—O3x84.67 (3)Ba1xvi—Mg2—Ba1xxii76.911 (11)
O3viii—Ba1—O3x95.33 (3)Ba1xxi—Mg2—Ba1xxii103.089 (11)
O3ix—Ba1—O3x180.00 (4)O3xiii—Mg2—Ba1xxiii135.374 (17)
O3i—Ba1—O3xi63.26 (4)O3xiv—Mg2—Ba1xxiii44.626 (17)
O3ii—Ba1—O3xi116.74 (4)O3xv—Mg2—Ba1xxiii135.374 (17)
O3iii—Ba1—O3xi84.67 (3)O3xvi—Mg2—Ba1xxiii44.626 (17)
O3iv—Ba1—O3xi95.33 (3)O3xvii—Mg2—Ba1xxiii82.16 (4)
O3v—Ba1—O3xi84.67 (3)O3xviii—Mg2—Ba1xxiii97.84 (4)
O3vi—Ba1—O3xi95.33 (3)Ba1xix—Mg2—Ba1xxiii103.089 (11)
O3vii—Ba1—O3xi122.92 (4)Ba1xx—Mg2—Ba1xxiii76.911 (11)
O3viii—Ba1—O3xi57.08 (4)Ba1xvi—Mg2—Ba1xxiii103.089 (11)
O3ix—Ba1—O3xi136.11 (5)Ba1xxi—Mg2—Ba1xxiii76.911 (11)
O3x—Ba1—O3xi43.89 (5)Ba1xxii—Mg2—Ba1xxiii180.0
O3i—Ba1—O3xii116.74 (4)C4xxiv—O3—Mg2xxv139.65 (12)
O3ii—Ba1—O3xii63.26 (4)C4xxiv—O3—Ba1xix94.64 (6)
O3iii—Ba1—O3xii95.33 (3)Mg2xxv—O3—Ba1xix105.89 (3)
O3iv—Ba1—O3xii84.67 (3)C4xxiv—O3—Ba1xxvi94.64 (6)
O3v—Ba1—O3xii95.33 (3)Mg2xxv—O3—Ba1xxvi105.89 (3)
O3vi—Ba1—O3xii84.67 (3)Ba1xix—O3—Ba1xxvi116.74 (4)
O3vii—Ba1—O3xii57.08 (4)O3xxvii—C4—O3xxviii119.842 (14)
O3viii—Ba1—O3xii122.92 (4)O3xxvii—C4—O3xxix119.842 (14)
O3ix—Ba1—O3xii43.89 (5)O3xxviii—C4—O3xxix119.842 (15)
O3x—Ba1—O3xii136.11 (5)O3xxvii—C4—Ba1xvi62.78 (5)
O3xi—Ba1—O3xii180.0O3xxviii—C4—Ba1xvi149.01 (13)
O3xiii—Mg2—O3xiv180.00 (6)O3xxix—C4—Ba1xvi62.78 (5)
O3xiii—Mg2—O3xv85.99 (5)O3xxvii—C4—Ba1xix149.01 (13)
O3xiv—Mg2—O3xv94.01 (5)O3xxviii—C4—Ba1xix62.78 (5)
O3xiii—Mg2—O3xvi94.01 (5)O3xxix—C4—Ba1xix62.78 (5)
O3xiv—Mg2—O3xvi85.99 (5)Ba1xvi—C4—Ba1xix98.87 (4)
O3xv—Mg2—O3xvi180.00 (6)O3xxvii—C4—Ba1xxii62.78 (5)
O3xiii—Mg2—O3xvii85.99 (5)O3xxviii—C4—Ba1xxii62.78 (5)
O3xiv—Mg2—O3xvii94.01 (5)O3xxix—C4—Ba1xxii149.01 (13)
O3xv—Mg2—O3xvii85.99 (5)Ba1xvi—C4—Ba1xxii98.87 (4)
O3xvi—Mg2—O3xvii94.01 (5)Ba1xix—C4—Ba1xxii98.87 (4)
O3xiii—Mg2—O3xviii94.01 (5)
Symmetry codes: (i) x+1/3, y+2/3, z+2/3; (ii) x1/3, y2/3, z+1/3; (iii) y2/3, x+y+2/3, z+2/3; (iv) y+2/3, xy2/3, z+1/3; (v) xy2/3, x4/3, z+2/3; (vi) x+y+2/3, x+4/3, z+1/3; (vii) xy+1/3, x1/3, z+2/3; (viii) x+y1/3, x+1/3, z+1/3; (ix) y2/3, x+y1/3, z+2/3; (x) y+2/3, xy+1/3, z+1/3; (xi) x4/3, y2/3, z+1/3; (xii) x+4/3, y+2/3, z+2/3; (xiii) y1/3, x+y+1/3, z+1/3; (xiv) y+1/3, xy1/3, z1/3; (xv) x+2/3, y+1/3, z+1/3; (xvi) x2/3, y1/3, z1/3; (xvii) xy1/3, x2/3, z+1/3; (xviii) x+y+1/3, x+2/3, z1/3; (xix) x+1/3, y+2/3, z1/3; (xx) x1/3, y2/3, z2/3; (xxi) x+2/3, y+1/3, z2/3; (xxii) x+1/3, y1/3, z1/3; (xxiii) x1/3, y+1/3, z2/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z1/3; (xxvii) x1, y1, z; (xxviii) y+1, xy, z; (xxix) x+y, x+1, z.
(norse_460) top
Crystal data top
C6Ba3Mg3O18Dx = 3.823 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3mCell parameters from 3849 reflections
a = 5.0256 (10) Åθ = 1.5–45°
c = 16.782 (6) ŵ = 8.20 mm1
V = 367.1 (2) Å3T = 440 K
Z = 1Prismatic
F(000) = 3840.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.027
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.5°, θmin = 12.5°
Tmin = 0.7, Tmax = 0.8h = 99
3849 measured reflectionsk = 910
413 independent reflectionsl = 3316
413 reflections with I > 2σ(I)
Refinement top
Refinement on F214 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.014 w = 1/[σ2(Fo2) + (0.0178P)2 + 0.1629P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.032(Δ/σ)max < 0.001
S = 1.12Δρmax = 0.81 e Å3
413 reflectionsΔρmin = 0.76 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.50000.01569 (5)
Mg20.00000.00000.00000.01248 (14)
O30.85367 (12)0.7073 (2)0.25763 (7)0.0299 (2)
C40.00000.00000.26075 (10)0.0127 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.01375 (5)0.01375 (5)0.01956 (7)0.00688 (3)0.0000.000
Mg20.0106 (2)0.0106 (2)0.0163 (3)0.00529 (10)0.0000.000
O30.0381 (5)0.0114 (3)0.0313 (4)0.00572 (16)0.00231 (16)0.0046 (3)
C40.0121 (3)0.0121 (3)0.0140 (5)0.00606 (16)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.9454 (8)Mg2—O3xviii2.0649 (11)
Ba1—O3ii2.9454 (8)Mg2—Ba1xix4.0301 (8)
Ba1—O3iii2.9454 (8)Mg2—Ba1xx4.0301 (8)
Ba1—O3iv2.9454 (8)Mg2—Ba1xxi4.0301 (8)
Ba1—O3v2.9455 (8)Mg2—Ba1xviii4.0301 (8)
Ba1—O3vi2.9455 (8)Mg2—Ba1xxii4.0301 (8)
Ba1—O3vii2.9455 (8)Mg2—Ba1xxiii4.0301 (8)
Ba1—O3viii2.9455 (8)O3—C4xxiv1.2748 (11)
Ba1—O3ix2.9455 (8)O3—Mg2xxv2.0649 (11)
Ba1—O3x2.9455 (8)O3—Ba1xx2.9454 (8)
Ba1—O3xi2.9455 (8)O3—Ba1xxvi2.9455 (8)
Ba1—O3xii2.9455 (8)C4—O3xxvii1.2748 (11)
Mg2—O3xiii2.0649 (11)C4—O3xxviii1.2748 (11)
Mg2—O3xiv2.0649 (11)C4—O3xxix1.2748 (11)
Mg2—O3xv2.0649 (11)C4—Ba1xviii3.3033 (10)
Mg2—O3xvi2.0649 (11)C4—Ba1xx3.3033 (10)
Mg2—O3xvii2.0649 (11)C4—Ba1xxiii3.3034 (10)
O3i—Ba1—O3ii180.0O3xiv—Mg2—O3xviii86.11 (5)
O3i—Ba1—O3iii57.19 (4)O3xv—Mg2—O3xviii93.89 (5)
O3ii—Ba1—O3iii122.81 (4)O3xvi—Mg2—O3xviii86.11 (5)
O3i—Ba1—O3iv122.81 (4)O3xvii—Mg2—O3xviii180.00 (7)
O3ii—Ba1—O3iv57.19 (4)O3xiii—Mg2—Ba1xix135.299 (18)
O3iii—Ba1—O3iv180.0O3xiv—Mg2—Ba1xix44.701 (18)
O3i—Ba1—O3v43.99 (4)O3xv—Mg2—Ba1xix135.299 (18)
O3ii—Ba1—O3v136.01 (4)O3xvi—Mg2—Ba1xix44.701 (18)
O3iii—Ba1—O3v95.57 (3)O3xvii—Mg2—Ba1xix81.92 (4)
O3iv—Ba1—O3v84.43 (3)O3xviii—Mg2—Ba1xix98.08 (4)
O3i—Ba1—O3vi136.01 (4)O3xiii—Mg2—Ba1xx44.701 (18)
O3ii—Ba1—O3vi43.99 (4)O3xiv—Mg2—Ba1xx135.299 (18)
O3iii—Ba1—O3vi84.43 (3)O3xv—Mg2—Ba1xx44.701 (18)
O3iv—Ba1—O3vi95.57 (3)O3xvi—Mg2—Ba1xx135.299 (18)
O3v—Ba1—O3vi180.0O3xvii—Mg2—Ba1xx98.08 (4)
O3i—Ba1—O3vii95.57 (3)O3xviii—Mg2—Ba1xx81.92 (4)
O3ii—Ba1—O3vii84.43 (3)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii43.99 (4)O3xiii—Mg2—Ba1xxi81.92 (4)
O3iv—Ba1—O3vii136.01 (4)O3xiv—Mg2—Ba1xxi98.08 (4)
O3v—Ba1—O3vii117.10 (5)O3xv—Mg2—Ba1xxi135.299 (18)
O3vi—Ba1—O3vii62.90 (5)O3xvi—Mg2—Ba1xxi44.701 (18)
O3i—Ba1—O3viii84.43 (3)O3xvii—Mg2—Ba1xxi135.299 (18)
O3ii—Ba1—O3viii95.57 (3)O3xviii—Mg2—Ba1xxi44.701 (18)
O3iii—Ba1—O3viii136.01 (4)Ba1xix—Mg2—Ba1xxi77.146 (18)
O3iv—Ba1—O3viii43.99 (4)Ba1xx—Mg2—Ba1xxi102.854 (18)
O3v—Ba1—O3viii62.90 (5)O3xiii—Mg2—Ba1xviii98.08 (4)
O3vi—Ba1—O3viii117.10 (5)O3xiv—Mg2—Ba1xviii81.92 (4)
O3vii—Ba1—O3viii180.00 (2)O3xv—Mg2—Ba1xviii44.701 (18)
O3i—Ba1—O3ix95.57 (3)O3xvi—Mg2—Ba1xviii135.299 (18)
O3ii—Ba1—O3ix84.43 (3)O3xvii—Mg2—Ba1xviii44.701 (18)
O3iii—Ba1—O3ix117.10 (5)O3xviii—Mg2—Ba1xviii135.299 (18)
O3iv—Ba1—O3ix62.90 (5)Ba1xix—Mg2—Ba1xviii102.854 (18)
O3v—Ba1—O3ix57.19 (4)Ba1xx—Mg2—Ba1xviii77.146 (18)
O3vi—Ba1—O3ix122.81 (4)Ba1xxi—Mg2—Ba1xviii180.0
O3vii—Ba1—O3ix95.57 (3)O3xiii—Mg2—Ba1xxii135.299 (18)
O3viii—Ba1—O3ix84.43 (3)O3xiv—Mg2—Ba1xxii44.701 (18)
O3i—Ba1—O3x84.43 (3)O3xv—Mg2—Ba1xxii81.92 (4)
O3ii—Ba1—O3x95.57 (3)O3xvi—Mg2—Ba1xxii98.08 (4)
O3iii—Ba1—O3x62.90 (5)O3xvii—Mg2—Ba1xxii135.299 (18)
O3iv—Ba1—O3x117.10 (5)O3xviii—Mg2—Ba1xxii44.701 (18)
O3v—Ba1—O3x122.81 (4)Ba1xix—Mg2—Ba1xxii77.146 (18)
O3vi—Ba1—O3x57.19 (4)Ba1xx—Mg2—Ba1xxii102.854 (19)
O3vii—Ba1—O3x84.43 (3)Ba1xxi—Mg2—Ba1xxii77.146 (18)
O3viii—Ba1—O3x95.57 (3)Ba1xviii—Mg2—Ba1xxii102.854 (18)
O3ix—Ba1—O3x180.0O3xiii—Mg2—Ba1xxiii44.701 (18)
O3i—Ba1—O3xi62.90 (5)O3xiv—Mg2—Ba1xxiii135.299 (18)
O3ii—Ba1—O3xi117.10 (5)O3xv—Mg2—Ba1xxiii98.08 (4)
O3iii—Ba1—O3xi84.43 (3)O3xvi—Mg2—Ba1xxiii81.92 (4)
O3iv—Ba1—O3xi95.57 (3)O3xvii—Mg2—Ba1xxiii44.701 (18)
O3v—Ba1—O3xi84.43 (3)O3xviii—Mg2—Ba1xxiii135.299 (18)
O3vi—Ba1—O3xi95.57 (3)Ba1xix—Mg2—Ba1xxiii102.854 (19)
O3vii—Ba1—O3xi122.81 (4)Ba1xx—Mg2—Ba1xxiii77.146 (18)
O3viii—Ba1—O3xi57.19 (4)Ba1xxi—Mg2—Ba1xxiii102.854 (18)
O3ix—Ba1—O3xi136.01 (4)Ba1xviii—Mg2—Ba1xxiii77.146 (18)
O3x—Ba1—O3xi43.99 (4)Ba1xxii—Mg2—Ba1xxiii180.0
O3i—Ba1—O3xii117.10 (5)C4xxiv—O3—Mg2xxv139.67 (11)
O3ii—Ba1—O3xii62.90 (5)C4xxiv—O3—Ba1xx94.67 (5)
O3iii—Ba1—O3xii95.57 (3)Mg2xxv—O3—Ba1xx105.75 (3)
O3iv—Ba1—O3xii84.43 (3)C4xxiv—O3—Ba1xxvi94.67 (5)
O3v—Ba1—O3xii95.57 (3)Mg2xxv—O3—Ba1xxvi105.75 (3)
O3vi—Ba1—O3xii84.43 (3)Ba1xx—O3—Ba1xxvi117.10 (5)
O3vii—Ba1—O3xii57.19 (4)O3xxvii—C4—O3xxviii119.834 (14)
O3viii—Ba1—O3xii122.81 (4)O3xxvii—C4—O3xxix119.831 (13)
O3ix—Ba1—O3xii43.99 (4)O3xxviii—C4—O3xxix119.831 (14)
O3x—Ba1—O3xii136.01 (4)O3xxvii—C4—Ba1xviii62.71 (4)
O3xi—Ba1—O3xii180.0O3xxviii—C4—Ba1xviii149.09 (11)
O3xiii—Mg2—O3xiv180.00 (5)O3xxix—C4—Ba1xviii62.71 (4)
O3xiii—Mg2—O3xv86.11 (5)O3xxvii—C4—Ba1xx149.09 (11)
O3xiv—Mg2—O3xv93.89 (5)O3xxviii—C4—Ba1xx62.71 (4)
O3xiii—Mg2—O3xvi93.89 (5)O3xxix—C4—Ba1xx62.71 (4)
O3xiv—Mg2—O3xvi86.11 (5)Ba1xviii—C4—Ba1xx99.05 (3)
O3xv—Mg2—O3xvi180.00 (5)O3xxvii—C4—Ba1xxiii62.71 (4)
O3xiii—Mg2—O3xvii86.11 (5)O3xxviii—C4—Ba1xxiii62.71 (4)
O3xiv—Mg2—O3xvii93.89 (5)O3xxix—C4—Ba1xxiii149.09 (11)
O3xv—Mg2—O3xvii86.11 (5)Ba1xviii—C4—Ba1xxiii99.05 (3)
O3xvi—Mg2—O3xvii93.89 (5)Ba1xx—C4—Ba1xxiii99.05 (3)
O3xiii—Mg2—O3xviii93.89 (5)
Symmetry codes: (i) x+1/3, y+2/3, z+2/3; (ii) x1/3, y2/3, z+1/3; (iii) y2/3, x+y+2/3, z+2/3; (iv) y+2/3, xy2/3, z+1/3; (v) xy2/3, x4/3, z+2/3; (vi) x+y+2/3, x+4/3, z+1/3; (vii) xy+1/3, x1/3, z+2/3; (viii) x+y1/3, x+1/3, z+1/3; (ix) y2/3, x+y1/3, z+2/3; (x) y+2/3, xy+1/3, z+1/3; (xi) x4/3, y2/3, z+1/3; (xii) x+4/3, y+2/3, z+2/3; (xiii) y1/3, x+y+1/3, z+1/3; (xiv) y+1/3, xy1/3, z1/3; (xv) xy1/3, x2/3, z+1/3; (xvi) x+y+1/3, x+2/3, z1/3; (xvii) x+2/3, y+1/3, z+1/3; (xviii) x2/3, y1/3, z1/3; (xix) x1/3, y2/3, z2/3; (xx) x+1/3, y+2/3, z1/3; (xxi) x+2/3, y+1/3, z2/3; (xxii) x1/3, y+1/3, z2/3; (xxiii) x+1/3, y1/3, z1/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z1/3; (xxvii) x1, y1, z; (xxviii) y+1, xy, z; (xxix) x+y, x+1, z.
(norse_480) top
Crystal data top
C6Ba3Mg3O18Dx = 3.821 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3mCell parameters from 3872 reflections
a = 5.027 (1) Åθ = 1.5–45°
c = 16.778 (3) ŵ = 8.20 mm1
V = 367.20 (16) Å3T = 480 K
Z = 1Prismatic
F(000) = 3840.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.029
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.6°, θmin = 12.5°
Tmin = 0.7, Tmax = 0.8h = 910
3872 measured reflectionsk = 1010
415 independent reflectionsl = 1633
414 reflections with I > 2σ(I)
Refinement top
Refinement on F214 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.015 w = 1/[σ2(Fo2) + (0.0175P)2 + 0.4063P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.034(Δ/σ)max < 0.001
S = 1.08Δρmax = 0.84 e Å3
415 reflectionsΔρmin = 0.78 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.50000.01625 (5)
Mg20.00000.00000.00000.01278 (15)
O30.85365 (13)0.7073 (3)0.25768 (8)0.0306 (2)
C40.00000.00000.26074 (10)0.0130 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.01419 (5)0.01419 (5)0.02038 (7)0.00709 (3)0.0000.000
Mg20.0108 (2)0.0108 (2)0.0167 (3)0.00542 (11)0.0000.000
O30.0382 (5)0.0119 (3)0.0329 (5)0.00596 (17)0.00260 (17)0.0052 (3)
C40.0121 (3)0.0121 (3)0.0148 (5)0.00607 (17)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.9463 (8)Mg2—O3xviii2.0645 (12)
Ba1—O3ii2.9463 (8)Mg2—Ba1xix4.0303 (5)
Ba1—O3iii2.9463 (8)Mg2—Ba1xx4.0303 (5)
Ba1—O3iv2.9463 (8)Mg2—Ba1xvi4.0303 (5)
Ba1—O3v2.9463 (8)Mg2—Ba1xxi4.0303 (5)
Ba1—O3vi2.9463 (8)Mg2—Ba1xxii4.0303 (5)
Ba1—O3vii2.9463 (8)Mg2—Ba1xxiii4.0303 (5)
Ba1—O3viii2.9463 (8)O3—C4xxiv1.2753 (12)
Ba1—O3ix2.9463 (8)O3—Mg2xxv2.0645 (12)
Ba1—O3x2.9463 (8)O3—Ba1xix2.9463 (8)
Ba1—O3xi2.9463 (8)O3—Ba1xxvi2.9463 (8)
Ba1—O3xii2.9463 (8)C4—O3xxvii1.2753 (12)
Mg2—O3xiii2.0645 (12)C4—O3xxviii1.2753 (12)
Mg2—O3xiv2.0645 (12)C4—O3xxix1.2753 (12)
Mg2—O3xv2.0645 (12)C4—Ba1xvi3.3038 (10)
Mg2—O3xvi2.0645 (12)C4—Ba1xix3.3038 (10)
Mg2—O3xvii2.0645 (12)C4—Ba1xxii3.3038 (10)
O3i—Ba1—O3ii180.0O3xiv—Mg2—O3xviii86.15 (6)
O3i—Ba1—O3iii57.18 (4)O3xv—Mg2—O3xviii93.85 (6)
O3ii—Ba1—O3iii122.82 (4)O3xvi—Mg2—O3xviii86.15 (6)
O3i—Ba1—O3iv122.82 (4)O3xvii—Mg2—O3xviii180.00 (6)
O3ii—Ba1—O3iv57.18 (4)O3xiii—Mg2—Ba1xix44.716 (18)
O3iii—Ba1—O3iv180.0O3xiv—Mg2—Ba1xix135.284 (18)
O3i—Ba1—O3v43.99 (5)O3xv—Mg2—Ba1xix98.12 (4)
O3ii—Ba1—O3v136.01 (5)O3xvi—Mg2—Ba1xix81.88 (4)
O3iii—Ba1—O3v95.57 (3)O3xvii—Mg2—Ba1xix44.717 (18)
O3iv—Ba1—O3v84.43 (3)O3xviii—Mg2—Ba1xix135.283 (18)
O3i—Ba1—O3vi136.01 (5)O3xiii—Mg2—Ba1xx135.284 (18)
O3ii—Ba1—O3vi43.99 (5)O3xiv—Mg2—Ba1xx44.716 (18)
O3iii—Ba1—O3vi84.43 (3)O3xv—Mg2—Ba1xx81.88 (4)
O3iv—Ba1—O3vi95.57 (3)O3xvi—Mg2—Ba1xx98.12 (4)
O3v—Ba1—O3vi180.0O3xvii—Mg2—Ba1xx135.283 (18)
O3i—Ba1—O3vii95.57 (3)O3xviii—Mg2—Ba1xx44.717 (18)
O3ii—Ba1—O3vii84.43 (3)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii43.99 (5)O3xiii—Mg2—Ba1xvi98.12 (4)
O3iv—Ba1—O3vii136.01 (5)O3xiv—Mg2—Ba1xvi81.88 (4)
O3v—Ba1—O3vii117.10 (5)O3xv—Mg2—Ba1xvi44.716 (18)
O3vi—Ba1—O3vii62.90 (5)O3xvi—Mg2—Ba1xvi135.284 (18)
O3i—Ba1—O3viii84.43 (3)O3xvii—Mg2—Ba1xvi44.718 (18)
O3ii—Ba1—O3viii95.57 (3)O3xviii—Mg2—Ba1xvi135.282 (18)
O3iii—Ba1—O3viii136.01 (5)Ba1xix—Mg2—Ba1xvi77.167 (12)
O3iv—Ba1—O3viii43.99 (5)Ba1xx—Mg2—Ba1xvi102.833 (12)
O3v—Ba1—O3viii62.90 (5)O3xiii—Mg2—Ba1xxi81.88 (4)
O3vi—Ba1—O3viii117.10 (5)O3xiv—Mg2—Ba1xxi98.12 (4)
O3vii—Ba1—O3viii180.00 (2)O3xv—Mg2—Ba1xxi135.284 (18)
O3i—Ba1—O3ix95.57 (3)O3xvi—Mg2—Ba1xxi44.716 (18)
O3ii—Ba1—O3ix84.43 (3)O3xvii—Mg2—Ba1xxi135.282 (18)
O3iii—Ba1—O3ix117.10 (5)O3xviii—Mg2—Ba1xxi44.718 (18)
O3iv—Ba1—O3ix62.90 (5)Ba1xix—Mg2—Ba1xxi102.833 (12)
O3v—Ba1—O3ix57.18 (4)Ba1xx—Mg2—Ba1xxi77.167 (12)
O3vi—Ba1—O3ix122.82 (4)Ba1xvi—Mg2—Ba1xxi180.0
O3vii—Ba1—O3ix95.57 (3)O3xiii—Mg2—Ba1xxii44.718 (18)
O3viii—Ba1—O3ix84.43 (3)O3xiv—Mg2—Ba1xxii135.282 (18)
O3i—Ba1—O3x84.43 (3)O3xv—Mg2—Ba1xxii44.718 (18)
O3ii—Ba1—O3x95.57 (3)O3xvi—Mg2—Ba1xxii135.282 (18)
O3iii—Ba1—O3x62.90 (5)O3xvii—Mg2—Ba1xxii98.12 (4)
O3iv—Ba1—O3x117.10 (5)O3xviii—Mg2—Ba1xxii81.88 (4)
O3v—Ba1—O3x122.82 (4)Ba1xix—Mg2—Ba1xxii77.167 (12)
O3vi—Ba1—O3x57.18 (4)Ba1xx—Mg2—Ba1xxii102.833 (12)
O3vii—Ba1—O3x84.43 (3)Ba1xvi—Mg2—Ba1xxii77.167 (12)
O3viii—Ba1—O3x95.57 (3)Ba1xxi—Mg2—Ba1xxii102.833 (12)
O3ix—Ba1—O3x180.0O3xiii—Mg2—Ba1xxiii135.282 (18)
O3i—Ba1—O3xi62.90 (5)O3xiv—Mg2—Ba1xxiii44.718 (18)
O3ii—Ba1—O3xi117.10 (5)O3xv—Mg2—Ba1xxiii135.282 (18)
O3iii—Ba1—O3xi84.43 (3)O3xvi—Mg2—Ba1xxiii44.718 (18)
O3iv—Ba1—O3xi95.57 (3)O3xvii—Mg2—Ba1xxiii81.88 (4)
O3v—Ba1—O3xi84.43 (3)O3xviii—Mg2—Ba1xxiii98.12 (4)
O3vi—Ba1—O3xi95.57 (3)Ba1xix—Mg2—Ba1xxiii102.833 (12)
O3vii—Ba1—O3xi122.82 (4)Ba1xx—Mg2—Ba1xxiii77.167 (12)
O3viii—Ba1—O3xi57.18 (4)Ba1xvi—Mg2—Ba1xxiii102.833 (12)
O3ix—Ba1—O3xi136.01 (5)Ba1xxi—Mg2—Ba1xxiii77.167 (12)
O3x—Ba1—O3xi43.99 (5)Ba1xxii—Mg2—Ba1xxiii180.0
O3i—Ba1—O3xii117.10 (5)C4xxiv—O3—Mg2xxv139.74 (12)
O3ii—Ba1—O3xii62.90 (5)C4xxiv—O3—Ba1xix94.64 (5)
O3iii—Ba1—O3xii95.57 (3)Mg2xxv—O3—Ba1xix105.74 (3)
O3iv—Ba1—O3xii84.43 (3)C4xxiv—O3—Ba1xxvi94.64 (5)
O3v—Ba1—O3xii95.57 (3)Mg2xxv—O3—Ba1xxvi105.74 (3)
O3vi—Ba1—O3xii84.43 (3)Ba1xix—O3—Ba1xxvi117.10 (5)
O3vii—Ba1—O3xii57.18 (4)O3xxvii—C4—O3xxviii119.838 (14)
O3viii—Ba1—O3xii122.82 (4)O3xxvii—C4—O3xxix119.838 (14)
O3ix—Ba1—O3xii43.99 (5)O3xxviii—C4—O3xxix119.838 (14)
O3x—Ba1—O3xii136.01 (5)O3xxvii—C4—Ba1xvi62.73 (5)
O3xi—Ba1—O3xii180.0O3xxviii—C4—Ba1xvi149.15 (12)
O3xiii—Mg2—O3xiv180.00 (6)O3xxix—C4—Ba1xvi62.73 (5)
O3xiii—Mg2—O3xv86.15 (6)O3xxvii—C4—Ba1xix149.15 (12)
O3xiv—Mg2—O3xv93.85 (6)O3xxviii—C4—Ba1xix62.73 (5)
O3xiii—Mg2—O3xvi93.85 (6)O3xxix—C4—Ba1xix62.73 (5)
O3xiv—Mg2—O3xvi86.15 (6)Ba1xvi—C4—Ba1xix99.07 (4)
O3xv—Mg2—O3xvi180.00 (6)O3xxvii—C4—Ba1xxii62.73 (5)
O3xiii—Mg2—O3xvii86.15 (6)O3xxviii—C4—Ba1xxii62.73 (5)
O3xiv—Mg2—O3xvii93.85 (6)O3xxix—C4—Ba1xxii149.15 (12)
O3xv—Mg2—O3xvii86.15 (6)Ba1xvi—C4—Ba1xxii99.07 (4)
O3xvi—Mg2—O3xvii93.85 (6)Ba1xix—C4—Ba1xxii99.07 (3)
O3xiii—Mg2—O3xviii93.85 (6)
Symmetry codes: (i) x+1/3, y+2/3, z+2/3; (ii) x1/3, y2/3, z+1/3; (iii) y2/3, x+y+2/3, z+2/3; (iv) y+2/3, xy2/3, z+1/3; (v) xy2/3, x4/3, z+2/3; (vi) x+y+2/3, x+4/3, z+1/3; (vii) xy+1/3, x1/3, z+2/3; (viii) x+y1/3, x+1/3, z+1/3; (ix) y2/3, x+y1/3, z+2/3; (x) y+2/3, xy+1/3, z+1/3; (xi) x4/3, y2/3, z+1/3; (xii) x+4/3, y+2/3, z+2/3; (xiii) y1/3, x+y+1/3, z+1/3; (xiv) y+1/3, xy1/3, z1/3; (xv) x+2/3, y+1/3, z+1/3; (xvi) x2/3, y1/3, z1/3; (xvii) xy1/3, x2/3, z+1/3; (xviii) x+y+1/3, x+2/3, z1/3; (xix) x+1/3, y+2/3, z1/3; (xx) x1/3, y2/3, z2/3; (xxi) x+2/3, y+1/3, z2/3; (xxii) x+1/3, y1/3, z1/3; (xxiii) x1/3, y+1/3, z2/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z1/3; (xxvii) x1, y1, z; (xxviii) y+1, xy, z; (xxix) x+y, x+1, z.
(norse_500) top
Crystal data top
C6Ba3Mg3O18Dx = 3.816 Mg m3
Mr = 845.01Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3mCell parameters from 4296 reflections
a = 5.0277 (4) Åθ = 1.5–45°
c = 16.7972 (14) ŵ = 8.19 mm1
V = 367.71 (7) Å3T = 500 K
Z = 1Prismatic
F(000) = 3840.06 × 0.03 × 0.03 mm
Data collection top
StoeStadiVari
diffractometer
Rint = 0.033
Absorption correction: numerical
(Stoe & Cie GmbH 2016)
θmax = 45.5°, θmin = 12.5°
Tmin = 0.7, Tmax = 0.8h = 910
4296 measured reflectionsk = 109
415 independent reflectionsl = 3318
415 reflections with I > 2σ(I)
Refinement top
Refinement on F214 parameters
Least-squares matrix: full0 restraints
R[F2 > 2σ(F2)] = 0.015 w = 1/[σ2(Fo2) + (0.018P)2 + 0.2798P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.035(Δ/σ)max < 0.001
S = 1.12Δρmax = 1.46 e Å3
415 reflectionsΔρmin = 0.81 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.00000.00000.50000.01686 (5)
Mg20.00000.00000.00000.01337 (15)
O30.85378 (13)0.7076 (3)0.25766 (8)0.0314 (3)
C40.00000.00000.26088 (11)0.0133 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.01471 (5)0.01471 (5)0.02116 (8)0.00736 (3)0.0000.000
Mg20.0113 (2)0.0113 (2)0.0175 (4)0.00566 (11)0.0000.000
O30.0397 (6)0.0120 (3)0.0335 (5)0.00599 (17)0.00250 (17)0.0050 (3)
C40.0124 (3)0.0124 (3)0.0150 (6)0.00621 (17)0.0000.000
Geometric parameters (Å, º) top
Ba1—O3i2.9474 (7)Mg2—O3xviii2.0666 (12)
Ba1—O3ii2.9474 (7)Mg2—Ba1xix4.0327 (2)
Ba1—O3iii2.9474 (7)Mg2—Ba1xx4.0327 (2)
Ba1—O3iv2.9474 (7)Mg2—Ba1xxi4.0327 (2)
Ba1—O3v2.9474 (7)Mg2—Ba1xviii4.0327 (2)
Ba1—O3vi2.9474 (7)Mg2—Ba1xxii4.0328 (2)
Ba1—O3vii2.9474 (7)Mg2—Ba1xxiii4.0328 (2)
Ba1—O3viii2.9474 (7)O3—C4xxiv1.2745 (12)
Ba1—O3ix2.9475 (7)O3—Mg2xxv2.0666 (12)
Ba1—O3x2.9475 (7)O3—Ba1xx2.9474 (7)
Ba1—O3xi2.9475 (7)O3—Ba1xxvi2.9475 (7)
Ba1—O3xii2.9475 (7)C4—O3xxvii1.2745 (12)
Mg2—O3xiii2.0666 (12)C4—O3xxviii1.2745 (12)
Mg2—O3xiv2.0666 (12)C4—O3xxix1.2745 (12)
Mg2—O3xv2.0666 (12)C4—Ba1xviii3.3061 (9)
Mg2—O3xvi2.0666 (12)C4—Ba1xx3.3061 (9)
Mg2—O3xvii2.0666 (12)C4—Ba1xxiii3.3061 (9)
O3i—Ba1—O3ii180.0O3xiv—Mg2—O3xviii86.13 (6)
O3i—Ba1—O3iii57.21 (4)O3xv—Mg2—O3xviii93.87 (6)
O3ii—Ba1—O3iii122.79 (5)O3xvi—Mg2—O3xviii86.13 (6)
O3i—Ba1—O3iv122.79 (5)O3xvii—Mg2—O3xviii179.97 (2)
O3ii—Ba1—O3iv57.21 (4)O3xiii—Mg2—Ba1xix135.297 (18)
O3iii—Ba1—O3iv180.0O3xiv—Mg2—Ba1xix44.703 (18)
O3i—Ba1—O3v43.94 (5)O3xv—Mg2—Ba1xix135.296 (18)
O3ii—Ba1—O3v136.06 (5)O3xvi—Mg2—Ba1xix44.704 (18)
O3iii—Ba1—O3v95.55 (3)O3xvii—Mg2—Ba1xix81.92 (4)
O3iv—Ba1—O3v84.45 (3)O3xviii—Mg2—Ba1xix98.08 (4)
O3i—Ba1—O3vi136.06 (5)O3xiii—Mg2—Ba1xx44.703 (18)
O3ii—Ba1—O3vi43.94 (5)O3xiv—Mg2—Ba1xx135.297 (18)
O3iii—Ba1—O3vi84.45 (3)O3xv—Mg2—Ba1xx44.704 (18)
O3iv—Ba1—O3vi95.55 (3)O3xvi—Mg2—Ba1xx135.296 (18)
O3v—Ba1—O3vi180.0O3xvii—Mg2—Ba1xx98.08 (4)
O3i—Ba1—O3vii95.55 (3)O3xviii—Mg2—Ba1xx81.92 (4)
O3ii—Ba1—O3vii84.45 (3)Ba1xix—Mg2—Ba1xx180.0
O3iii—Ba1—O3vii43.94 (5)O3xiii—Mg2—Ba1xxi81.92 (4)
O3iv—Ba1—O3vii136.06 (5)O3xiv—Mg2—Ba1xxi98.08 (4)
O3v—Ba1—O3vii117.06 (5)O3xv—Mg2—Ba1xxi135.296 (18)
O3vi—Ba1—O3vii62.94 (5)O3xvi—Mg2—Ba1xxi44.704 (18)
O3i—Ba1—O3viii84.45 (3)O3xvii—Mg2—Ba1xxi135.297 (18)
O3ii—Ba1—O3viii95.55 (3)O3xviii—Mg2—Ba1xxi44.703 (18)
O3iii—Ba1—O3viii136.06 (5)Ba1xix—Mg2—Ba1xxi77.124 (5)
O3iv—Ba1—O3viii43.94 (5)Ba1xx—Mg2—Ba1xxi102.876 (5)
O3v—Ba1—O3viii62.94 (5)O3xiii—Mg2—Ba1xviii98.08 (4)
O3vi—Ba1—O3viii117.06 (5)O3xiv—Mg2—Ba1xviii81.92 (4)
O3vii—Ba1—O3viii180.0O3xv—Mg2—Ba1xviii44.704 (18)
O3i—Ba1—O3ix95.54 (3)O3xvi—Mg2—Ba1xviii135.296 (18)
O3ii—Ba1—O3ix84.46 (3)O3xvii—Mg2—Ba1xviii44.703 (18)
O3iii—Ba1—O3ix117.06 (5)O3xviii—Mg2—Ba1xviii135.297 (18)
O3iv—Ba1—O3ix62.94 (5)Ba1xix—Mg2—Ba1xviii102.876 (5)
O3v—Ba1—O3ix57.21 (4)Ba1xx—Mg2—Ba1xviii77.124 (5)
O3vi—Ba1—O3ix122.79 (4)Ba1xxi—Mg2—Ba1xviii180.0
O3vii—Ba1—O3ix95.54 (3)O3xiii—Mg2—Ba1xxii135.296 (18)
O3viii—Ba1—O3ix84.46 (3)O3xiv—Mg2—Ba1xxii44.704 (18)
O3i—Ba1—O3x84.46 (3)O3xv—Mg2—Ba1xxii81.92 (4)
O3ii—Ba1—O3x95.54 (3)O3xvi—Mg2—Ba1xxii98.08 (4)
O3iii—Ba1—O3x62.94 (5)O3xvii—Mg2—Ba1xxii135.296 (18)
O3iv—Ba1—O3x117.06 (5)O3xviii—Mg2—Ba1xxii44.704 (18)
O3v—Ba1—O3x122.79 (4)Ba1xix—Mg2—Ba1xxii77.124 (5)
O3vi—Ba1—O3x57.21 (4)Ba1xx—Mg2—Ba1xxii102.876 (5)
O3vii—Ba1—O3x84.46 (3)Ba1xxi—Mg2—Ba1xxii77.124 (5)
O3viii—Ba1—O3x95.54 (3)Ba1xviii—Mg2—Ba1xxii102.876 (5)
O3ix—Ba1—O3x180.00 (5)O3xiii—Mg2—Ba1xxiii44.704 (18)
O3i—Ba1—O3xi62.94 (5)O3xiv—Mg2—Ba1xxiii135.296 (18)
O3ii—Ba1—O3xi117.06 (5)O3xv—Mg2—Ba1xxiii98.08 (4)
O3iii—Ba1—O3xi84.46 (3)O3xvi—Mg2—Ba1xxiii81.92 (4)
O3iv—Ba1—O3xi95.54 (3)O3xvii—Mg2—Ba1xxiii44.704 (18)
O3v—Ba1—O3xi84.46 (3)O3xviii—Mg2—Ba1xxiii135.296 (18)
O3vi—Ba1—O3xi95.54 (3)Ba1xix—Mg2—Ba1xxiii102.876 (5)
O3vii—Ba1—O3xi122.79 (4)Ba1xx—Mg2—Ba1xxiii77.124 (5)
O3viii—Ba1—O3xi57.21 (4)Ba1xxi—Mg2—Ba1xxiii102.876 (5)
O3ix—Ba1—O3xi136.06 (5)Ba1xviii—Mg2—Ba1xxiii77.124 (5)
O3x—Ba1—O3xi43.94 (5)Ba1xxii—Mg2—Ba1xxiii180.0
O3i—Ba1—O3xii117.06 (5)C4xxiv—O3—Mg2xxv139.61 (12)
O3ii—Ba1—O3xii62.94 (5)C4xxiv—O3—Ba1xx94.72 (6)
O3iii—Ba1—O3xii95.54 (3)Mg2xxv—O3—Ba1xx105.74 (3)
O3iv—Ba1—O3xii84.46 (3)C4xxiv—O3—Ba1xxvi94.72 (6)
O3v—Ba1—O3xii95.54 (3)Mg2xxv—O3—Ba1xxvi105.74 (3)
O3vi—Ba1—O3xii84.46 (3)Ba1xx—O3—Ba1xxvi117.06 (5)
O3vii—Ba1—O3xii57.21 (4)O3xxvii—C4—O3xxviii119.823 (15)
O3viii—Ba1—O3xii122.79 (4)O3xxvii—C4—O3xxix119.821 (15)
O3ix—Ba1—O3xii43.94 (5)O3xxviii—C4—O3xxix119.821 (15)
O3x—Ba1—O3xii136.06 (5)O3xxvii—C4—Ba1xviii62.68 (5)
O3xi—Ba1—O3xii180.0O3xxviii—C4—Ba1xviii148.97 (12)
O3xiii—Mg2—O3xiv180.00 (6)O3xxix—C4—Ba1xviii62.68 (5)
O3xiii—Mg2—O3xv86.13 (6)O3xxvii—C4—Ba1xx148.97 (12)
O3xiv—Mg2—O3xv93.87 (6)O3xxviii—C4—Ba1xx62.68 (5)
O3xiii—Mg2—O3xvi93.87 (6)O3xxix—C4—Ba1xx62.68 (5)
O3xiv—Mg2—O3xvi86.13 (6)Ba1xviii—C4—Ba1xx98.99 (4)
O3xv—Mg2—O3xvi180.00 (6)O3xxvii—C4—Ba1xxiii62.68 (5)
O3xiii—Mg2—O3xvii86.13 (6)O3xxviii—C4—Ba1xxiii62.68 (5)
O3xiv—Mg2—O3xvii93.87 (6)O3xxix—C4—Ba1xxiii148.97 (12)
O3xv—Mg2—O3xvii86.13 (6)Ba1xviii—C4—Ba1xxiii98.99 (4)
O3xvi—Mg2—O3xvii93.87 (6)Ba1xx—C4—Ba1xxiii98.99 (4)
O3xiii—Mg2—O3xviii93.87 (6)
Symmetry codes: (i) x+1/3, y+2/3, z+2/3; (ii) x1/3, y2/3, z+1/3; (iii) y2/3, x+y+2/3, z+2/3; (iv) y+2/3, xy2/3, z+1/3; (v) xy2/3, x4/3, z+2/3; (vi) x+y+2/3, x+4/3, z+1/3; (vii) xy+1/3, x1/3, z+2/3; (viii) x+y1/3, x+1/3, z+1/3; (ix) y2/3, x+y1/3, z+2/3; (x) y+2/3, xy+1/3, z+1/3; (xi) x4/3, y2/3, z+1/3; (xii) x+4/3, y+2/3, z+2/3; (xiii) y1/3, x+y+1/3, z+1/3; (xiv) y+1/3, xy1/3, z1/3; (xv) xy1/3, x2/3, z+1/3; (xvi) x+y+1/3, x+2/3, z1/3; (xvii) x+2/3, y+1/3, z+1/3; (xviii) x2/3, y1/3, z1/3; (xix) x1/3, y2/3, z2/3; (xx) x+1/3, y+2/3, z1/3; (xxi) x+2/3, y+1/3, z2/3; (xxii) x1/3, y+1/3, z2/3; (xxiii) x+1/3, y1/3, z1/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z1/3; (xxvii) x1, y1, z; (xxviii) y+1, xy, z; (xxix) x+y, x+1, z.
 

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